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Caroltal – Wikipedia

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</button> <ul id="toc-Referenser-sublist" class="vector-toc-list"> <li id="toc-Noter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Noter"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Noter</span> </div> </a> <ul id="toc-Noter-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Externa_länkar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externa_länkar"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Externa länkar</span> </div> </a> <ul id="toc-Externa_länkar-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Innehåll" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Växla innehållsförteckningen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Växla innehållsförteckningen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Caroltal</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Gå till en artikel på ett annat språk. Tillgänglig på 9 språk" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-9" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">9 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Carol-Zahl" title="Carol-Zahl – tyska" lang="de" hreflang="de" data-title="Carol-Zahl" data-language-autonym="Deutsch" data-language-local-name="tyska" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Nombre_de_Carol" title="Nombre de Carol – franska" lang="fr" hreflang="fr" data-title="Nombre de Carol" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%94%D5%A5%D6%80%D5%B8%D5%AC%D5%AB_%D5%A9%D5%AB%D5%BE" title="Քերոլի թիվ – armeniska" lang="hy" hreflang="hy" data-title="Քերոլի թիվ" data-language-autonym="Հայերեն" data-language-local-name="armeniska" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_di_Carol" title="Numero di Carol – italienska" lang="it" hreflang="it" data-title="Numero di Carol" data-language-autonym="Italiano" data-language-local-name="italienska" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Carol-sz%C3%A1mok" title="Carol-számok – ungerska" lang="hu" hreflang="hu" data-title="Carol-számok" data-language-autonym="Magyar" data-language-local-name="ungerska" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AD%E3%83%A3%E3%83%AD%E3%83%AB%E6%95%B0" title="キャロル数 – japanska" lang="ja" hreflang="ja" data-title="キャロル数" data-language-autonym="日本語" data-language-local-name="japanska" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE_%D0%9A%D1%8D%D1%80%D0%BE%D0%BB%D0%B0" title="Число Кэрола – ryska" lang="ru" hreflang="ru" data-title="Число Кэрола" data-language-autonym="Русский" data-language-local-name="ryska" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE_%D0%9A%D0%B5%D1%80%D0%BE%D0%BB" title="Число Керол – ukrainska" lang="uk" hreflang="uk" data-title="Число Керол" data-language-autonym="Українська" data-language-local-name="ukrainska" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8D%A1%E7%BE%85%E7%88%BE%E8%B3%AA%E6%95%B8" title="卡羅爾質數 – kinesiska" lang="zh" hreflang="zh" data-title="卡羅爾質數" data-language-autonym="中文" data-language-local-name="kinesiska" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q819137#sitelinks-wikipedia" title="Redigera interwikilänkar" class="wbc-editpage">Redigera länkar</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namnrymder"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Caroltal" title="Visa innehållssidan [c]" accesskey="c"><span>Artikel</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskussion:Caroltal&amp;action=edit&amp;redlink=1" rel="discussion" class="new" title="Diskussion om innehållssidan [inte skriven än] [t]" accesskey="t"><span>Diskussion</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Ändra språkvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">svenska</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Visningar"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Caroltal"><span>Läs</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Caroltal&amp;veaction=edit" title="Redigera denna sida [v]" accesskey="v"><span>Redigera</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Caroltal&amp;action=edit" title="Redigera wikitexten för den här sidan [e]" accesskey="e"><span>Redigera wikitext</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Caroltal&amp;action=history" title="Tidigare versioner av sidan [h]" accesskey="h"><span>Visa historik</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sidverktyg"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Verktyg" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Verktyg</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Verktyg</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">dölj</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Fler alternativ" > <div class="vector-menu-heading"> Åtgärder </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Caroltal"><span>Läs</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Caroltal&amp;veaction=edit" title="Redigera denna sida [v]" accesskey="v"><span>Redigera</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Caroltal&amp;action=edit" title="Redigera wikitexten för den här sidan [e]" accesskey="e"><span>Redigera wikitext</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Caroltal&amp;action=history"><span>Visa historik</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Allmänt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:L%C3%A4nkar_hit/Caroltal" title="Lista över alla wikisidor som länkar hit [j]" accesskey="j"><span>Sidor som länkar hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:Senaste_relaterade_%C3%A4ndringar/Caroltal" rel="nofollow" title="Visa senaste ändringarna av sidor som den här sidan länkar till [k]" accesskey="k"><span>Relaterade ändringar</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:Specialsidor" title="Lista över alla specialsidor [q]" accesskey="q"><span>Specialsidor</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Caroltal&amp;oldid=54379693" title="Permanent länk till den här versionen av sidan"><span>Permanent länk</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Caroltal&amp;action=info" title="Mer information om denna sida"><span>Sidinformation</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:Citera&amp;page=Caroltal&amp;id=54379693&amp;wpFormIdentifier=titleform" title="Information om hur den här artikeln kan användas som referens"><span>Använd som referens</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&amp;url=https%3A%2F%2Fsv.wikipedia.org%2Fwiki%2FCaroltal"><span>Hämta förkortad url</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&amp;url=https%3A%2F%2Fsv.wikipedia.org%2Fwiki%2FCaroltal"><span>Ladda ner QR-kod</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Skriv ut/exportera </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Special:Bok&amp;bookcmd=book_creator&amp;referer=Caroltal"><span>Skapa en bok</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&amp;page=Caroltal&amp;action=show-download-screen"><span>Ladda ned som PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Caroltal&amp;printable=yes" title="Utskriftsvänlig version av den här sidan [p]" accesskey="p"><span>Utskriftsvänlig version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> På andra projekt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q819137" title="Länk till anslutet databasobjekt [g]" accesskey="g"><span>Wikidata-objekt</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Sidverktyg"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">dölj</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Från Wikipedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Omdirigerad från <a href="/w/index.php?title=Carolprimtal&amp;redirect=no" class="mw-redirect" title="Carolprimtal">Carolprimtal</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sv" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fil:Caroltal.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Caroltal.jpg/300px-Caroltal.jpg" decoding="async" width="300" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Caroltal.jpg/450px-Caroltal.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/7/7c/Caroltal.jpg 2x" data-file-width="584" data-file-height="302" /></a><figcaption>Ett caroltal, det andra i ordningen.</figcaption></figure> <p><b>Caroltal</b> är ett <a href="/wiki/Heltal" title="Heltal">heltal</a> på formen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4^{n}-2^{n+1}-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>&#x2212;<!-- − --></mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>&#x2212;<!-- − --></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4^{n}-2^{n+1}-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7159b7ae821c23d9f447c4afc49042147ccf021a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.706ex; height:2.843ex;" alt="{\displaystyle 4^{n}-2^{n+1}-1}"></span>. En ekvivalent formel är <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (2^{n}-1)^{2}-2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>&#x2212;<!-- − --></mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>&#x2212;<!-- − --></mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2^{n}-1)^{2}-2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62e13727d2e3ee73c698a1e7efc04b562f49847f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.25ex; height:3.176ex;" alt="{\displaystyle (2^{n}-1)^{2}-2}"></span>. </p><p>De första Caroltalen är: </p> <dl><dd><a href="/wiki/%E2%88%921_(tal)" title="−1 (tal)">−1</a>, <a href="/wiki/7_(tal)" title="7 (tal)">7</a>, <a href="/wiki/47_(tal)" title="47 (tal)">47</a>, <a href="/wiki/223_(tal)" title="223 (tal)">223</a>, <a href="/w/index.php?title=959_(tal)&amp;action=edit&amp;redlink=1" class="new" title="959 (tal) [inte skriven än]">959</a>, <a href="/w/index.php?title=3967_(tal)&amp;action=edit&amp;redlink=1" class="new" title="3967 (tal) [inte skriven än]">3967</a>, <a href="/w/index.php?title=16127_(tal)&amp;action=edit&amp;redlink=1" class="new" title="16127 (tal) [inte skriven än]">16127</a>, <a href="/w/index.php?title=65023_(tal)&amp;action=edit&amp;redlink=1" class="new" title="65023 (tal) [inte skriven än]">65023</a>, <a href="/w/index.php?title=261119_(tal)&amp;action=edit&amp;redlink=1" class="new" title="261119 (tal) [inte skriven än]">261119</a>, <a href="/w/index.php?title=1046527_(tal)&amp;action=edit&amp;redlink=1" class="new" title="1046527 (tal) [inte skriven än]">1046527</a>, <a href="/w/index.php?title=4190207_(tal)&amp;action=edit&amp;redlink=1" class="new" title="4190207 (tal) [inte skriven än]">4190207</a>, <a href="/w/index.php?title=16769023_(tal)&amp;action=edit&amp;redlink=1" class="new" title="16769023 (tal) [inte skriven än]">16769023</a>, <a href="/w/index.php?title=67092479_(tal)&amp;action=edit&amp;redlink=1" class="new" title="67092479 (tal) [inte skriven än]">67092479</a>, <a href="/w/index.php?title=268402687_(tal)&amp;action=edit&amp;redlink=1" class="new" title="268402687 (tal) [inte skriven än]">268402687</a>, <a href="/w/index.php?title=1073676287_(tal)&amp;action=edit&amp;redlink=1" class="new" title="1073676287 (tal) [inte skriven än]">1073676287</a>, <a href="/w/index.php?title=4294836223_(tal)&amp;action=edit&amp;redlink=1" class="new" title="4294836223 (tal) [inte skriven än]">4294836223</a>, <a href="/w/index.php?title=17179607039_(tal)&amp;action=edit&amp;redlink=1" class="new" title="17179607039 (tal) [inte skriven än]">17179607039</a>, <a href="/w/index.php?title=68718952447_(tal)&amp;action=edit&amp;redlink=1" class="new" title="68718952447 (tal) [inte skriven än]">68718952447</a>, <a href="/w/index.php?title=274876858367_(tal)&amp;action=edit&amp;redlink=1" class="new" title="274876858367 (tal) [inte skriven än]">274876858367</a>, <a href="/w/index.php?title=1099509530623_(tal)&amp;action=edit&amp;redlink=1" class="new" title="1099509530623 (tal) [inte skriven än]">1099509530623</a>, <a href="/w/index.php?title=4398042316799_(tal)&amp;action=edit&amp;redlink=1" class="new" title="4398042316799 (tal) [inte skriven än]">4398042316799</a>, <a href="/w/index.php?title=17592177655807_(tal)&amp;action=edit&amp;redlink=1" class="new" title="17592177655807 (tal) [inte skriven än]">17592177655807</a>, … (talföljd <a href="//oeis.org/A093112" class="extiw" title="oeis:A093112">A093112</a> i <a href="/wiki/N%C3%A4tuppslagsverket_%C3%B6ver_heltalsf%C3%B6ljder" title="Nätuppslagsverket över heltalsföljder">OEIS</a>)</dd></dl> <p>Caroltal studerades först av <a href="/w/index.php?title=Cletus_Emmanuel&amp;action=edit&amp;redlink=1" class="new" title="Cletus Emmanuel [inte skriven än]">Cletus Emmanuel</a>, som namngav dem efter en vän, <a href="/w/index.php?title=Carol_G._Kirnon&amp;action=edit&amp;redlink=1" class="new" title="Carol G. Kirnon [inte skriven än]">Carol G. Kirnon</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-reference-link-bracket">[</span>1<span class="cite-reference-link-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-reference-link-bracket">[</span>2<span class="cite-reference-link-bracket">]</span></a></sup> </p><p>För <i>n</i> &gt; 2 är den binära representationen av Caroltal av det <i>n</i>:te Caroltalet <i>n</i> − 2 på varandra följande ettor, en nolla i mitten, och <i>n</i> + 1 fler ettor i rad. Det kan uttryckas algebraiskt med: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i\neq n+2}^{2n}2^{i-1}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>&#x2211;<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>&#x2260;<!-- ≠ --></mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> </mrow> </munderover> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>&#x2212;<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i\neq n+2}^{2n}2^{i-1}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7514c52afc64a74640a2b54dc786cbd219ada74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:10.029ex; height:7.843ex;" alt="{\displaystyle \sum _{i\neq n+2}^{2n}2^{i-1}.}"></span></dd></dl> <p>Så till exempel är 47 lika med 101111 i <a href="/wiki/Bin%C3%A4ra_talsystemet" title="Binära talsystemet">binära talsystemet</a> och 223 är 11011111 i det binära talsystemet etcetera. Skillnaden mellan det 2<i>n</i>:te <a href="/wiki/Mersennetal" class="mw-redirect" title="Mersennetal">Mersennetalet</a> och det <i>n</i>:te Caroltalet är <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{n+1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{n+1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87ec7da881b9da391c503b68a69a46ba3c43e189" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.481ex; height:2.676ex;" alt="{\displaystyle 2^{n+1}}"></span>. Detta ger ännu ett ekvivalent uttryck för Caroltal, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (2^{2n}-1)-2^{n+1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> </mrow> </msup> <mo>&#x2212;<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>&#x2212;<!-- − --></mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2^{2n}-1)-2^{n+1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb20b290c45411b2009ac22d918d9281ad0643ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.337ex; height:3.176ex;" alt="{\displaystyle (2^{2n}-1)-2^{n+1}}"></span>. Skillnaden mellan det <i>n</i>:te <a href="/wiki/Kyneatal" title="Kyneatal">Kyneatalet</a> och det <i>n</i>:te Caroltalet är den (<i>n</i> + 2):te <a href="/wiki/Tv%C3%A5potens" title="Tvåpotens">tvåpotensen</a>. </p><p>Från och med 7 är vart tredje Caroltal delbart med 7. För ett Caroltal för att också vara ett <a href="/wiki/Primtal" title="Primtal">primtal</a>, dess index <i>n</i> kan inte vara av formen 3<i>x</i> + 2 för <i>x</i> &gt; 0. </p><p>De första Caroltalen som även är primtal (<a href="/wiki/Carolprimtal" class="mw-redirect" title="Carolprimtal">Carolprimtal</a>) är: </p> <dl><dd><a href="/wiki/7_(tal)" title="7 (tal)">7</a>, <a href="/wiki/47_(tal)" title="47 (tal)">47</a>, <a href="/wiki/223_(tal)" title="223 (tal)">223</a>, <a href="/w/index.php?title=3967_(tal)&amp;action=edit&amp;redlink=1" class="new" title="3967 (tal) [inte skriven än]">3967</a>, <a href="/w/index.php?title=16127_(tal)&amp;action=edit&amp;redlink=1" class="new" title="16127 (tal) [inte skriven än]">16127</a>, <a href="/w/index.php?title=1046527_(tal)&amp;action=edit&amp;redlink=1" class="new" title="1046527 (tal) [inte skriven än]">1046527</a>, <a href="/w/index.php?title=16769023_(tal)&amp;action=edit&amp;redlink=1" class="new" title="16769023 (tal) [inte skriven än]">16769023</a>, <a href="/w/index.php?title=1073676287_(tal)&amp;action=edit&amp;redlink=1" class="new" title="1073676287 (tal) [inte skriven än]">1073676287</a>, <a href="/w/index.php?title=68718952447_(tal)&amp;action=edit&amp;redlink=1" class="new" title="68718952447 (tal) [inte skriven än]">68718952447</a>, <a href="/w/index.php?title=274876858367_(tal)&amp;action=edit&amp;redlink=1" class="new" title="274876858367 (tal) [inte skriven än]">274876858367</a>, <a href="/w/index.php?title=4398042316799_(tal)&amp;action=edit&amp;redlink=1" class="new" title="4398042316799 (tal) [inte skriven än]">4398042316799</a>, <a href="/w/index.php?title=1125899839733759_(tal)&amp;action=edit&amp;redlink=1" class="new" title="1125899839733759 (tal) [inte skriven än]">1125899839733759</a>, <a href="/w/index.php?title=18014398241046527_(tal)&amp;action=edit&amp;redlink=1" class="new" title="18014398241046527 (tal) [inte skriven än]">18014398241046527</a>, <a href="/w/index.php?title=1298074214633706835075030044377087_(tal)&amp;action=edit&amp;redlink=1" class="new" title="1298074214633706835075030044377087 (tal) [inte skriven än]">1298074214633706835075030044377087</a>, … (talföljd <a href="//oeis.org/A091516" class="extiw" title="oeis:A091516">A091516</a> i <a href="/wiki/N%C3%A4tuppslagsverket_%C3%B6ver_heltalsf%C3%B6ljder" title="Nätuppslagsverket över heltalsföljder">OEIS</a>)</dd></dl> <p>Från och med juli 2007 är det största Caroltalet som även är primtal <i>n</i> = 253987, och har 152916 siffror.<sup id="cite_ref-Entry_for_253987th_Carol_number_3-0" class="reference"><a href="#cite_note-Entry_for_253987th_Carol_number-3"><span class="cite-reference-link-bracket">[</span>3<span class="cite-reference-link-bracket">]</span></a></sup><sup id="cite_ref-Carol_Primes_and_Kynea_Primes_4-0" class="reference"><a href="#cite_note-Carol_Primes_and_Kynea_Primes-4"><span class="cite-reference-link-bracket">[</span>4<span class="cite-reference-link-bracket">]</span></a></sup> Det upptäcktes av <sup id="cite_ref-Entry_for_253987th_Carol_number_3-1" class="reference"><a href="#cite_note-Entry_for_253987th_Carol_number-3"><span class="cite-reference-link-bracket">[</span>3<span class="cite-reference-link-bracket">]</span></a></sup><sup id="cite_ref-Carol_Primes_and_Kynea_Primes_4-1" class="reference"><a href="#cite_note-Carol_Primes_and_Kynea_Primes-4"><span class="cite-reference-link-bracket">[</span>4<span class="cite-reference-link-bracket">]</span></a></sup> maj 2007 med hjälp av programmen MultiSieve och PrimeFormGW. Det är det 40:e Carolprimtalet. </p><p>Det 7:e Caroltalet och 5:e Carolprimtalet, 16127, är även primtal när dess siffror är omvända (<a href="/wiki/Emirp" class="mw-redirect" title="Emirp">emirp</a>), så det är det lägsta Carolemirp.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-reference-link-bracket">[</span>5<span class="cite-reference-link-bracket">]</span></a></sup> Det 12:e Caroltalet och 7:e Carolprimtalet, 16769023, är också ett Carolemirp.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-reference-link-bracket">[</span>6<span class="cite-reference-link-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Referenser">Referenser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Caroltal&amp;veaction=edit&amp;section=1" title="Redigera avsnitt: Referenser" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Caroltal&amp;action=edit&amp;section=1" title="Redigera avsnitts källkod: Referenser"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li></ul> <dl><dd><span class="plainlinks"><i>Den här artikeln är helt eller delvis baserad på material från <a href="/wiki/Engelskspr%C3%A5kiga_Wikipedia" title="Engelskspråkiga Wikipedia">engelskspråkiga Wikipedia</a>, <a class="external text" href="https://en.wikipedia.org/wiki/Carol_number">Carol number</a>, <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Carol_number&amp;oldid=560015478">20 december 2013</a>.</i></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Noter">Noter</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Caroltal&amp;veaction=edit&amp;section=2" title="Redigera avsnitt: Noter" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Caroltal&amp;action=edit&amp;section=2" title="Redigera avsnitts källkod: Noter"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <span class="reference-text"><a rel="nofollow" class="external text" href="http://primes.utm.edu/bios/page.php?id=374">Cletus Emmanuel</a> at <a href="/w/index.php?title=Prime_Pages&amp;action=edit&amp;redlink=1" class="new" title="Prime Pages [inte skriven än]">Prime Pages</a></span> </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <span class="reference-text"><a rel="nofollow" class="external text" href="http://tech.groups.yahoo.com/group/primenumbers/message/14584">Message to Yahoo primenumbers group</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110603214602/http://tech.groups.yahoo.com/group/primenumbers/message/14584">Arkiverad</a> 3 juni 2011 hämtat från the <a href="/wiki/Internet_Archive#Wayback_Machine" title="Internet Archive">Wayback Machine</a>. from Cletus Emmanuel</span> </li> <li id="cite_note-Entry_for_253987th_Carol_number-3">^ [<a href="#cite_ref-Entry_for_253987th_Carol_number_3-0"><small>a</small></a> <a href="#cite_ref-Entry_for_253987th_Carol_number_3-1"><small>b</small></a>] <span class="reference-text"><a rel="nofollow" class="external text" href="http://primes.utm.edu/primes/page.php?id=80384">Entry for 253987th Carol number</a> at <a href="/w/index.php?title=Prime_Pages&amp;action=edit&amp;redlink=1" class="new" title="Prime Pages [inte skriven än]">Prime Pages</a></span> </li> <li id="cite_note-Carol_Primes_and_Kynea_Primes-4">^ [<a href="#cite_ref-Carol_Primes_and_Kynea_Primes_4-0"><small>a</small></a> <a href="#cite_ref-Carol_Primes_and_Kynea_Primes_4-1"><small>b</small></a>] <span class="reference-text"><a rel="nofollow" class="external text" href="http://harvey563.tripod.com/Carol_Kynea.txt">Carol Primes and Kynea Primes</a> by Steven Harvey</span> </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> <span class="reference-text"><a rel="nofollow" class="external text" href="http://primes.utm.edu/curios/page.php/16127.html">Prime Curios 16127</a> at <a href="/w/index.php?title=Prime_Pages&amp;action=edit&amp;redlink=1" class="new" title="Prime Pages [inte skriven än]">Prime Pages</a></span> </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> <span class="reference-text"><a rel="nofollow" class="external text" href="http://primes.utm.edu/curios/page.php/16769023.html">Prime Curios 16769023</a> at <a href="/w/index.php?title=Prime_Pages&amp;action=edit&amp;redlink=1" class="new" title="Prime Pages [inte skriven än]">Prime Pages</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Externa_länkar"><span id="Externa_l.C3.A4nkar"></span>Externa länkar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Caroltal&amp;veaction=edit&amp;section=3" title="Redigera avsnitt: Externa länkar" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Caroltal&amp;action=edit&amp;section=3" title="Redigera avsnitts källkod: Externa länkar"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation mathworld" id="Reference-Mathworld-Near-Square_Prime"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a>, "<a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>", <i><a href="/wiki/Mathworld" title="Mathworld">MathWorld</a></i>. <span style="font-size:.95em;font-weight:bold;color:var(--color-subtle, #54595d);">(engelska)</span></span></li> <li><a rel="nofollow" class="external text" href="http://primes.utm.edu/primes/page.php?id=73109">Prime Database entry for Carol (226749)</a></li> <li><a rel="nofollow" class="external text" href="http://primes.utm.edu/primes/page.php?id=77385">Prime Database entry for Carol (248949)</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r56287950">.mw-parser-output table.navbox{border:#aaa 1px solid;width:100%;margin:auto;margin-top:1em;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output link+table.navbox{margin-top:-1px}.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow,.mw-parser-output table.navbox 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title="Naturliga tal">Naturliga tal</a> (ℕ)</span></th></tr><tr style="height:2px;"><td></td></tr><tr><td class="navbox-group" style=";;">&#160;Heltalspotenser</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Akillestal" title="Akillestal">Akilles</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Tv%C3%A5potens" title="Tvåpotens">Tvåpotens</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Tiopotens" title="Tiopotens">Tiopotens</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kvadrat_(aritmetik)" title="Kvadrat (aritmetik)">Kvadrat</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kub_(aritmetik)" title="Kub (aritmetik)">Kub</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Fj%C3%A4rde_potens" title="Fjärde potens">Fjärde potens</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Femte_potens" title="Femte potens">Femte potens</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Primtalspotens" title="Primtalspotens">Primtalspotens</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">&#160;Av formen <i>a</i>&#160;×&#160;2<sup><i>b</i></sup>&#160;±&#160;1</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Cullental" title="Cullental">Cullen</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Dubbelt_Mersennetal" title="Dubbelt Mersennetal">Dubbelt Mersenne</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Fermattal" title="Fermattal">Fermat</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Mersennetal" class="mw-redirect" title="Mersennetal">Mersenne</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Prothtal" title="Prothtal">Proth</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Thabittal" title="Thabittal">Thabit</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Woodalltal" title="Woodalltal">Woodall</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Andra polynomtal</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a class="mw-selflink selflink">Carol</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Hilberttal" title="Hilberttal">Hilbert</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kyneatal" title="Kyneatal">Kynea</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Leylandtal" title="Leylandtal">Leyland</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Eulers_lyckotal" title="Eulers lyckotal">Eulers lyckotal</a></div></td></tr><tr 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style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;"><a href="/wiki/Kodning" title="Kodning">Kodrelaterade</a></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Meertenstal" title="Meertenstal">Meertens</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;"><a href="/wiki/Figurtal" title="Figurtal">Figurtal</a></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r56287950"></div><table class="navbox-subgroup" style="width:100%;border-spacing:0;;;;"><tbody><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;"><a href="/wiki/2D" class="mw-redirect" title="2D">2D</a></div></td><td 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title="Hexagontal">6∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Heptagontal" title="Heptagontal">7∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Oktogontal" title="Oktogontal">8∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Nonagontal" title="Nonagontal">9∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Dekagontal" title="Dekagontal">10∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Hendekagontal" title="Hendekagontal">11∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Dodekagontal" title="Dodekagontal">12∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Tridekagontal" title="Tridekagontal">13∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Tetradekagontal" title="Tetradekagontal">14∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Pentadekagontal" title="Pentadekagontal">15∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Hexadekagontal" title="Hexadekagontal">16∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Heptadekagontal" title="Heptadekagontal">17∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Oktodekagontal" title="Oktodekagontal">18∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Nonadekagontal" title="Nonadekagontal">19∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Ikosagontal" title="Ikosagontal">20∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Ikosihenagontal" title="Ikosihenagontal">21∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Ikosidigontal" title="Ikosidigontal">22∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Ikositrigontal" title="Ikositrigontal">23∡</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Ikositetragontal" title="Ikositetragontal">24∡</a><span 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style="font-weight:bold;">&#160;· </span> <a href="/wiki/Centrerat_hexagontal" title="Centrerat hexagontal">Centrerad hexagon</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Centrerat_heptagontal" title="Centrerat heptagontal">Centrerad heptagon</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Centrerat_oktogontal" title="Centrerat oktogontal">Centrerad oktogon</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Centrerat_nonagontal" title="Centrerat nonagontal">Centrerad nonagon</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Centrerat_dekagontal" title="Centrerat dekagontal">Centrerad dekagon</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Stj%C3%A4rntal" title="Stjärntal">Stjärna</a></div></td></tr></tbody></table><div></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;"><a href="/wiki/3D" class="mw-redirect" title="3D">3D</a></div></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r56287950"></div><table class="navbox-subgroup" style="width:100%;border-spacing:0;;;;"><tbody><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;"><a href="/wiki/Polyedertal" class="mw-redirect" title="Polyedertal">Icke-centrerade</a></div></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Tetraedertal" title="Tetraedertal">Tetraeder</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kub_(aritmetik)" title="Kub (aritmetik)">Kubiktal</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Oktaedertal" title="Oktaedertal">Oktaeder</a><span 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style="font-weight:bold;">&#160;· </span> <a href="/wiki/Centrerat_dodekaedertal" title="Centrerat dodekaedertal">Centrerad dodekaeder</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Centrerat_ikosaedertal" title="Centrerat ikosaedertal">Centrerad ikosaeder</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;"><a href="/wiki/Pyramidtal" title="Pyramidtal">Pyramidtal</a></div></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Pentagonalt_pyramidtal" title="Pentagonalt pyramidtal">Pentagonal pyramid</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Hexagonalt_pyramidtal" title="Hexagonalt pyramidtal">Hexagonal pyramid</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Heptagonalt_pyramidtal" title="Heptagonalt pyramidtal">Heptagonal pyramid</a></div></td></tr></tbody></table><div></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;"><a href="/wiki/4D" class="mw-redirect" title="4D">4D</a></div></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Tesserakttal" title="Tesserakttal">Tesserakt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kvadrattriangul%C3%A4rt_tal" title="Kvadrattriangulärt tal">Kvadrattriangulärt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kubkvadrat" class="mw-redirect" title="Kubkvadrat">Kubkvadrat</a></div></td></tr></tbody></table><div></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;"><a href="/wiki/Pseudoprimtal" title="Pseudoprimtal">Pseudoprimtal</a></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Carmichaeltal" title="Carmichaeltal">Carmichael</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Elliptiskt_pseudoprimtal" title="Elliptiskt pseudoprimtal">Elliptiskt pseudoprimtal</a><span style="font-weight:bold;">&#160;· </span></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;"><a href="/wiki/Kombinatorik" title="Kombinatorik">Kombinatoriska tal</a></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Belltal" title="Belltal">Bell</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Catalantal" title="Catalantal">Catalan</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Fuss%E2%80%93Catalantal" title="Fuss–Catalantal">Fuss–Catalan</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Motzkintal" title="Motzkintal">Motzkin</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Schr%C3%B6dertal" title="Schrödertal">Schröder</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;"><a href="/wiki/Aritmetisk_funktion" title="Aritmetisk funktion">Aritmetiska funktioner</a></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r56287950"></div><table class="navbox-subgroup" style="width:100%;border-spacing:0;;;;"><tbody><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;">Genom egenskaper hos <a href="/wiki/Sigmafunktionen" title="Sigmafunktionen">σ(<i>n</i>)</a></div></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Ymnigt_tal" title="Ymnigt tal">Ymnigt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/N%C3%A4stan-perfekt_tal" title="Nästan-perfekt tal">Nästan-perfekt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Aritmetiskt_tal" title="Aritmetiskt tal">Aritmetiskt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kolossalt_ymnigt_tal" title="Kolossalt ymnigt tal">Kolossalt ymnigt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Descartestal" title="Descartestal">Descartes</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Hemiperfekt_tal" title="Hemiperfekt tal">Hemiperfekt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Mycket_ymnigt_tal" title="Mycket ymnigt tal">Mycket ymnigt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Hyperperfekt_tal" title="Hyperperfekt tal">Hyperperfekt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Multiperfekt_tal" title="Multiperfekt tal">Multiperfekt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Perfekt_tal" title="Perfekt tal">Perfekt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Primitivt_ymnigt_tal" title="Primitivt ymnigt tal">Primitivt ymnigt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kvasiperfekt_tal" title="Kvasiperfekt tal">Kvasiperfekt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Superymnigt_tal" title="Superymnigt tal">Superymnigt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Mycket_h%C3%B6gt_sammansatt_tal" title="Mycket högt sammansatt tal">Mycket högt sammansatt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Superperfekt_tal" title="Superperfekt tal">Superfekt</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;">Genom egenskaper hos <a href="/wiki/Aritmetisk_funktion" title="Aritmetisk funktion">Ω(<i>n</i>)</a></div></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/N%C3%A4stan-primtal" title="Nästan-primtal">Nästan-primtal</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Semiprimtal" title="Semiprimtal">Semiprimtal</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;">Genom egenskaper hos <a href="/wiki/Sigmafunktionen#Definition" title="Sigmafunktionen">s(<i>n</i>)</a></div></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/V%C3%A4nskapligt_tal" title="Vänskapligt tal">Vänskapligt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kvasiv%C3%A4nskapligt_tal" title="Kvasivänskapligt tal">Kvasivänskapligt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Defekt_tal" title="Defekt tal">Defekt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Semiperfekt_tal" title="Semiperfekt tal">Semiperfekt</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";padding-left:0em;padding-right:0em;;"><div style="padding:0em 0.75em;">Övriga tal</div></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Euklidestal" title="Euklidestal">Euklides</a></div></td></tr></tbody></table><div></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Andra <a href="/wiki/Primtalsfaktor" title="Primtalsfaktor">primtalsfaktor</a>- eller <br /><a href="/wiki/Delbarhet" title="Delbarhet">delbarhetsrelarerade</a> tal</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Erd%C5%91s%E2%80%93Woodstal" title="Erdős–Woodstal">Erdős–Woods</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Frugalt_tal" title="Frugalt tal">Frugalt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Giugatal" title="Giugatal">Giuga</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Mycket_sammansatt_tal" title="Mycket sammansatt tal">Mycket sammansatt</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Lucas%E2%80%93Carmichaeltal" title="Lucas–Carmichaeltal">Lucas–Carmichael</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Rektangeltal" title="Rektangeltal">Rektangel</a><span style="font-weight:bold;">&#160;· </span> 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style="font-weight:bold;">&#160;· </span> <a href="/wiki/Glada_tal" title="Glada tal">Glada</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Harshadtal" title="Harshadtal">Harshad</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Kaprekartal" title="Kaprekartal">Kaprekar</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Keithtal" title="Keithtal">Keith</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Lychreltal" class="mw-redirect" title="Lychreltal">Lychrel</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Palindromtal" title="Palindromtal">Palindrom</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Smarandache%E2%80%93Wellintal" title="Smarandache–Wellintal">Smarandache–Wellin</a><span style="font-weight:bold;">&#160;· </span> <a href="/wiki/Vampyrtal" title="Vampyrtal">Vampyr</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;"><a 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