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href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97&returntoquery=variant%3Dzh-sg" title="我们推荐您创建账号并登录，但这不是强制性的"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97&returntoquery=variant%3Dzh-sg" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" lang="zh-Hans-SG" dir="ltr"> <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-性質" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#性質"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>性质</span> </div> </a> <ul id="toc-性質-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-類似數列" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#類似數列"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>类似数列</span> </div> </a> <ul id="toc-類似數列-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-歷史" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#歷史"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>历史</span> </div> </a> <ul id="toc-歷史-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考資料" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考資料"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>参考资料</span> </div> </a> <ul id="toc-參考資料-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="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="zh-Hans-SG" dir="ltr"> <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="开关目录" > <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">开关目录</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" lang="zh-Hans-SG" dir="ltr"><span class="mw-page-title-main">米安-邱拉数列</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="zh-Hans-SG" dir="ltr"> <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="前往另一种语言写成的文章。10种语言可用" > <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-10" 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">10种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AA%D8%AA%D8%A7%D9%84%D9%8A%D8%A9_%D9%85%D9%8A%D8%A7%D9%86_-_%D8%AA%D8%B4%D9%88%D9%84%D8%A7" title="متتالية ميان - تشولا – 阿拉伯语" lang="ar" hreflang="ar" data-title="متتالية ميان - تشولا" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Mian%E2%80%93Chowla-Folge" title="Mian–Chowla-Folge – 德语" lang="de" hreflang="de" data-title="Mian–Chowla-Folge" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Sucesi%C3%B2un_ed_Mian-Chowla" title="Sucesiòun ed Mian-Chowla – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Sucesiòun ed Mian-Chowla" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Mian%E2%80%93Chowla_sequence" title="Mian–Chowla sequence – 英语" lang="en" hreflang="en" data-title="Mian–Chowla sequence" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Suite_de_Mian-Chowla" title="Suite de Mian-Chowla – 法语" lang="fr" hreflang="fr" data-title="Suite de Mian-Chowla" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Mian%E2%80%93Chowla-sorozat" title="Mian–Chowla-sorozat – 匈牙利语" lang="hu" hreflang="hu" data-title="Mian–Chowla-sorozat" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Successione_di_Mian-Chowla" title="Successione di Mian-Chowla – 意大利语" lang="it" hreflang="it" data-title="Successione di Mian-Chowla" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9F%E3%82%A2%E3%83%B3%EF%BC%9D%E3%83%81%E3%83%A7%E3%82%A6%E3%83%A9%E6%95%B0%E5%88%97" title="ミアン＝チョウラ数列 – 日语" lang="ja" hreflang="ja" data-title="ミアン＝チョウラ数列" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_Mian-Chowla" title="Număr Mian-Chowla – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Număr Mian-Chowla" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Mian%E2%80%93Chowlas_f%C3%B6ljd" title="Mian–Chowlas följd – 瑞典语" lang="sv" hreflang="sv" data-title="Mian–Chowlas följd" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</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/Q3976569#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</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="命名空间"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" lang="zh-Hans-SG" dir="ltr"> <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/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" rel="discussion" title="关于此页面的讨论[t]" accesskey="t"><span>讨论</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " lang="zh-Hans-SG" dir="ltr"> <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="更改语言变体" > <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">新加坡简体</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" lang="zh-Hans-SG" dir="ltr"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="ca-variants-zh mw-list-item"><a href="/zh/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh" hreflang="zh"><span>不转换</span></a></li><li id="ca-varlang-1" class="ca-variants-zh-Hans mw-list-item"><a href="/zh-hans/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh-Hans" hreflang="zh-Hans"><span>简体</span></a></li><li id="ca-varlang-2" class="ca-variants-zh-Hant mw-list-item"><a href="/zh-hant/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh-Hant" hreflang="zh-Hant"><span>繁體</span></a></li><li id="ca-varlang-3" class="ca-variants-zh-Hans-CN mw-list-item"><a href="/zh-cn/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh-Hans-CN" hreflang="zh-Hans-CN"><span>大陆简体</span></a></li><li id="ca-varlang-4" class="ca-variants-zh-Hant-HK mw-list-item"><a href="/zh-hk/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh-Hant-HK" hreflang="zh-Hant-HK"><span>香港繁體</span></a></li><li id="ca-varlang-5" class="ca-variants-zh-Hant-MO mw-list-item"><a href="/zh-mo/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh-Hant-MO" hreflang="zh-Hant-MO"><span>澳門繁體</span></a></li><li id="ca-varlang-6" class="ca-variants-zh-Hans-MY mw-list-item"><a href="/zh-my/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh-Hans-MY" hreflang="zh-Hans-MY"><span>大马简体</span></a></li><li id="ca-varlang-7" class="selected ca-variants-zh-Hans-SG mw-list-item"><a href="/zh-sg/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh-Hans-SG" hreflang="zh-Hans-SG"><span>新加坡简体</span></a></li><li id="ca-varlang-8" class="ca-variants-zh-Hant-TW mw-list-item"><a href="/zh-tw/%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97" lang="zh-Hant-TW" hreflang="zh-Hant-TW"><span>臺灣正體</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="查看"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" lang="zh-Hans-SG" dir="ltr"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" 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.ambox-protection{border-left-color:#a2a9b1!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ambox{border-left-color:#36c!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-No_footnotes plainlinks metadata ambox ambox-style" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/File:Text_document_with_red_question_mark.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">此条目已<a href="/wiki/Wikipedia:%E5%88%97%E6%98%8E%E4%BE%86%E6%BA%90" class="mw-redirect" title="Wikipedia:列明来源">列出参考文献</a>，但<b>因为没有<a href="/wiki/Help:%E8%84%9A%E6%B3%A8" title="Help:脚注">文内引注</a>而使来源仍然不明</b>。<span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2018年1月11日</span>)</i></small><span class="hide-when-compact"><br /><small>请加上合适的文内引注来<a class="external text" href="https://zh.wikipedia.org/w/index.php?title=%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97&action=edit">改善这篇条目</a>。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <p><b>米安-邱拉数列</b>(Mian-Chowla sequence)是以<a href="/wiki/%E9%80%92%E5%BD%92" title="递归">递归</a>方式定义的<a href="/wiki/%E6%95%B4%E6%95%B8%E6%95%B8%E5%88%97" title="整数数列">整数数列</a>，其首项为 </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 a_{1}=1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{1}=1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44a7b0185c92dd00a09ce4f4f34002c535dbccf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.192ex; height:2.509ex;" alt="{\displaystyle a_{1}=1.}"></span></dd></dl> <p>而对于<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 n>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n>1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee74e1cc07e7041edf0fcbd4481f5cd32ad17b64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n>1}"></span>，<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 a_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/790f9209748c2dca7ed7b81932c37c02af1dbc31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.448ex; height:2.009ex;" alt="{\displaystyle a_{n}}"></span>是对于所有不大于<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>的<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 i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>和<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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>，以下的二项和 </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 a_{i}+a_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i}+a_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3109b4ff3350e89d66d20d353384cc034fd6602" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.009ex; height:2.676ex;" alt="{\displaystyle a_{i}+a_{j}}"></span></dd></dl> <p>均不重复的最小整数。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="性質"><span id=".E6.80.A7.E8.B3.AA"></span>性质</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97&action=edit&section=1" title="编辑章节：性质"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>第一项为<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 a_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbf42ecda092975c9c69dae84e16182ba5fe2e07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle a_{1}}"></span>，其二项和只有一个1 + 1 = 2，数列的下一项是<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 a_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/270580da7333505d9b73697417d0543c43c98b9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle a_{2}}"></span>，其二项和有2, 3, 4，都不重复。第三项<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 a_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/602d08dd865689204f563ce6f0de095c8ca67410" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle a_{3}}"></span>不能是3，因为若<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 a_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/602d08dd865689204f563ce6f0de095c8ca67410" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle a_{3}}"></span>是3，就会有重复的二项和1 + 3 = 2 + 2 = 4，可得到<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 a_{3}=4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{3}=4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/072da6e065cb1a047adb474623885f90bc7ca541" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.545ex; height:2.509ex;" alt="{\displaystyle a_{3}=4}"></span>，二项和为2, 3, 4, 5, 6, 8。米安-邱拉数列的前几项是 </p> <dl><dd><a href="/wiki/1" title="1">1</a>, <a href="/wiki/2" title="2">2</a>, <a href="/wiki/4" title="4">4</a>, <a href="/wiki/8" title="8">8</a>, <a href="/wiki/13" title="13">13</a>, <a href="/wiki/21" title="21">21</a>, <a href="/wiki/31" title="31">31</a>, <a href="/wiki/45" title="45">45</a>, <a href="/wiki/66" title="66">66</a>, <a href="/wiki/81" title="81">81</a>, <a href="/wiki/97" title="97">97</a>, <a href="/wiki/123" title="123">123</a>, <a href="/wiki/148" title="148">148</a>, <a href="/wiki/182" title="182">182</a>, <a href="/wiki/204" title="204">204</a>, <a href="/wiki/252" title="252">252</a>, <a href="/wiki/290" title="290">290</a>, 361, 401, 475, ... （<a href="/wiki/%E6%95%B4%E6%95%B8%E6%95%B8%E5%88%97%E7%B7%9A%E4%B8%8A%E5%A4%A7%E5%85%A8" title="整数数列线上大全">OEIS</a>数列<a href="//oeis.org/A005282" class="extiw" title="oeis:A005282">A005282</a>）.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="類似數列"><span id=".E9.A1.9E.E4.BC.BC.E6.95.B8.E5.88.97"></span>类似数列</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97&action=edit&section=2" title="编辑章节：类似数列"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>若定义<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 a_{1}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{1}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dac97b493b8da48c509596f28389f8dc2b13853" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.545ex; height:2.509ex;" alt="{\displaystyle a_{1}=0}"></span>，所得的数列相近，不过每一项都比米安-邱拉数列要少1（0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, ... <a rel="nofollow" class="external text" href="//oeis.org/A025582">A025582</a>）。 </p> <div class="mw-heading mw-heading2"><h2 id="歷史"><span id=".E6.AD.B7.E5.8F.B2"></span>历史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97&action=edit&section=3" title="编辑章节：历史"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>此数列是由<a href="/w/index.php?title=%E9%98%BF%E5%B8%83%E6%9D%9C%E7%88%BE%C2%B7%E9%A6%AC%E5%9F%BA%E5%BE%B7%C2%B7%E7%B1%B3%E5%AE%89&action=edit&redlink=1" class="new" title="阿布杜尔·马基德·米安（页面不存在）">阿布杜尔·马基德·米安</a>和<span class="ilh-all" data-orig-title="薩爾瓦達曼·邱拉" data-lang-code="en" data-lang-name="英语" data-foreign-title="Sarvadaman Chowla"><span class="ilh-page"><a href="/w/index.php?title=%E8%96%A9%E7%88%BE%E7%93%A6%E9%81%94%E6%9B%BC%C2%B7%E9%82%B1%E6%8B%89&action=edit&redlink=1" class="new" title="萨尔瓦达曼·邱拉（页面不存在）">萨尔瓦达曼·邱拉</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Sarvadaman_Chowla" class="extiw" title="en:Sarvadaman Chowla"><span lang="en" dir="auto">Sarvadaman Chowla</span></a></span>）</span></span>所发现。 </p> <div class="mw-heading mw-heading2"><h2 id="參考資料"><span id=".E5.8F.83.E8.80.83.E8.B3.87.E6.96.99"></span>参考资料</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B1%B3%E5%AE%89-%E9%82%B1%E6%8B%89%E6%95%B8%E5%88%97&action=edit&section=4" title="编辑章节：参考资料"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>S. R. Finch, <i>Mathematical Constants</i>, Cambridge (2003): Section 2.20.2</li> <li>R. K. Guy <i>Unsolved Problems in Number Theory</i>, New York: Springer (2003)</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="" lang="zh-Hans-SG" dir="ltr">检索自“<a dir="ltr" href="https://zh.wikipedia.org/w/index.php?title=米安-邱拉數列&oldid=58137054">https://zh.wikipedia.org/w/index.php?title=米安-邱拉數列&oldid=58137054</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:%E9%A1%B5%E9%9D%A2%E5%88%86%E7%B1%BB" title="Special:页面分类">分类</a>：<ul><li><a href="/wiki/Category:%E6%95%B4%E6%95%B0%E6%95%B0%E5%88%97" title="Category:整数数列">整数数列</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">隐藏分类：<ul><li><a 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