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A007953 - OEIS
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <html> <head> <link rel="stylesheet" href="/styles.css"> <meta name="format-detection" content="telephone=no"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta name="keywords" content="OEIS,integer sequences,Sloane" /> <title>A007953 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A007953" function redir() { var host = document.location.hostname; if(host != "oeis.org" && host != "127.0.0.1" && !/^([0-9.]+)$/.test(host) && host != "localhost" && host != "localhost.localdomain") { document.location = "https"+":"+"//"+"oeis"+".org/" + myURL; } } function sf() { if(document.location.pathname == "/" && document.f) document.f.q.focus(); } </script> </head> <body bgcolor=#ffffff onload="redir();sf()"> <div class=loginbar> <div class=login> <a href="/login?redirect=%2fA007953">login</a> </div> </div> <div class=center><div class=top> <center> <div class=donors> The OEIS is supported by <a href="http://oeisf.org/#DONATE">the many generous donors to the OEIS Foundation</a>. </div> <div class=banner> <a href="/"><img class=banner border="0" width="600" src="/banner2021.jpg" alt="A007953 - OEIS"></a> </div> </center> </div></div> <div class=center><div class=pagebody> <div class=searchbarcenter> <form name=f action="/search" method="GET"> <div class=searchbargreet> <div class=searchbar> <div class=searchq> <input class=searchbox maxLength=1024 name=q value="" title="Search Query"> </div> <div class=searchsubmit> <input type=submit value="Search" name=go> </div> <div class=hints> <span class=hints><a href="/hints.html">Hints</a></span> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> A007953 </div> <div class=seqname> Digital sum (i.e., sum of digits) of n; also called digsum(n). </div> </div> <div class=scorerefs> 1115 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14, 15</div> <div class=seqdatalinks> (<a href="/A007953/list">list</a>; <a href="/A007953/graph">graph</a>; <a href="/search?q=A007953+-id:A007953">refs</a>; <a href="/A007953/listen">listen</a>; <a href="/history?seq=A007953">history</a>; <a href="/search?q=id:A007953&fmt=text">text</a>; <a href="/A007953/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,3</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>Do not confuse with the digital root of n, <a href="/A010888" title="Digital root of n (repeatedly add the digits of n until a single digit is reached).">A010888</a> (first term that differs is a(19)).</div> <div class=sectline>Also the fixed point of the morphism 0 -> {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, 1 -> {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 2 -> {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, etc. - <a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, Jul 27 2006</div> <div class=sectline>For n < 100 equal to (floor(n/10) + n mod 10) = <a href="/A076314" title="a(n) = floor(n/10) + (n mod 10).">A076314</a>(n). - <a href="/wiki/User:Hieronymus_Fischer">Hieronymus Fischer</a>, Jun 17 2007</div> <div class=sectline>It appears that a(n) is the position of 10*n in the ordered set of numbers obtained by inserting/placing one digit anywhere in the digits of n (except a zero before 1st digit). For instance, for n=2, the resulting set is (12, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 42, 52, 62, 72, 82, 92) where 20 is at position 2, so a(2) = 2. - <a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Aug 01 2022</div> <div class=sectline>Also the total number of beads required to represent n on a Russian abacus (schoty). - <a href="/wiki/User:P._Christopher_Staecker">P. Christopher Staecker</a>, Mar 31 2023</div> <div class=sectline>a(n) / a(2n) <= 5 with equality iff n is in <a href="/A169964" title="Numbers whose decimal expansion contains only 0's and 5's.">A169964</a>, while a(n) / a(3n) is unbounded, since if n = (10^k + 2)/3, then a(n) = 3*k+1, a(3n) = 3, so a(n) / a(3n) = k + 1/3 -> oo when k->oo (see Diophante link). - <a href="/wiki/User:Bernard_Schott">Bernard Schott</a>, Apr 29 2023</div> </div> </div> <div class=section> <div class=sectname>REFERENCES</div> <div class=sectbody> <div class=sectline>Krassimir Atanassov, On the 16th Smarandache Problem, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 1, 36-38.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>N. J. A. Sloane, <a href="/A007953/b007953.txt">Table of n, a(n) for n = 0..10000</a></div> <div class=sectline>Krassimir Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">On Some of Smarandache's Problems</a>.</div> <div class=sectline>Jean-Luc Baril, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p178">Classical sequences revisited with permutations avoiding dotted pattern</a>, Electronic Journal of Combinatorics, Vol. 18 (2011), #P178.</div> <div class=sectline>F. M. Dekking, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Dekking/dek25.html">The Thue-Morse Sequence in Base 3/2</a>, J. Int. Seq., Vol. 26 (2023), Article 23.2.3.</div> <div class=sectline>Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a1-pot-pourri/5453-a1762-des-chiffres-a-la-moulinette">A1762, Des chiffres 脿 la moulinette</a> (in French).</div> <div class=sectline>Ernesto Estrada and Puri Pereira-Ramos, <a href="https://doi.org/10.1155/2018/9893867">Spatial 'Artistic' Networks: From Deconstructing Integer-Functions to Visual Arts</a>, Complexity, Vol. 2018 (2018), Article ID 9893867.</div> <div class=sectline>A. O. Gel'fond, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa13/aa13115.pdf">Sur les nombres qui ont des propri茅t茅s additives et multiplicatives donn茅es</a> (French) Acta Arith., Vol. 13 (1967/1968), pp. 259-265. MR0220693 (36 #3745)</div> <div class=sectline>Christian Mauduit and Andr谩s S谩rk枚zy, <a href="http://dx.doi.org/10.1006/jnth.1998.2229">On the arithmetic structure of sets characterized by sum of digits properties</a> J. Number Theory, Vol. 61 , No. 1 (1996), pp. 25-38. MR1418316 (97g:11107)</div> <div class=sectline>Christian Mauduit and Andr谩s S谩rk枚zy, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa81/aa8122.pdf"> On the arithmetic structure of the integers whose sum of digits is fixed</a>, Acta Arith., Vol. 81, No. 2 (1997), pp. 145-173. MR1456239 (99a:11096)</div> <div class=sectline>Kerry Mitchell, <a href="http://kerrymitchellart.com/articles/Spirolateral-Type_Images_from_Integer_Sequences.pdf">Spirolateral-Type Images from Integer Sequences</a>, 2013.</div> <div class=sectline>Kerry Mitchell, <a href="/A007953/a007953.jpg">Spirolateral image for this sequence</a> . [taken, with permission, from the Spirolateral-Type Images from Integer Sequences article]</div> <div class=sectline>Jan-Christoph Puchta and J眉rgen Spilker, <a href="http://dx.doi.org/10.1007/s00591-002-0048-4">Altes und Neues zur Quersumme</a>, Mathematische Semesterberichte, Vol. 49 (2002), pp. 209-226.</div> <div class=sectline>Jan-Christoph Puchta and J眉rgen Spilker, <a href="http://www.math.uni-rostock.de/~schlage-puchta/papers/Quersumme.pdf">Altes und Neues zur Quersumme</a>.</div> <div class=sectline>Maxwell Schneider and Robert Schneider, <a href="https://arxiv.org/abs/1807.06710">Digit sums and generating functions</a>, arXiv:1807.06710 [math.NT], 2018.</div> <div class=sectline>Jeffrey O. Shallit, <a href="http://www.jstor.org/stable/2322179">Problem 6450</a>, Advanced Problems, The American Mathematical Monthly, Vol. 91, No. 1 (1984), pp. 59-60; <a href="http://www.jstor.org/stable/2322523">Two series, solution to Problem 6450</a>, ibid., Vol. 92, No. 7 (1985), pp. 513-514.</div> <div class=sectline>Vladimir Shevelev, <a href="http://journals.impan.pl/aa/Inf/126-3-1.html">Compact integers and factorials</a>, Acta Arith., Vol. 126, No. 3 (2007), pp. 195-236 (cf. pp. 205-206).</div> <div class=sectline>Robert Walker, <a href="http://robertinventor.com/ftswiki/Self_Similar_Sloth_Canon_Number_Sequences">Self Similar Sloth Canon Number Sequences</a>.</div> <div class=sectline>Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>.</div> <div class=sectline>Wikipedia, <a href="http://en.wikipedia.org/wiki/Digit_sum">Digit sum</a>.</div> <div class=sectline><a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>a(<a href="/A051885" title="Smallest number whose sum of digits is n.">A051885</a>(n)) = n.</div> <div class=sectline>a(n) <= 9(log_10(n)+1). - <a href="/wiki/User:Stefan_Steinerberger">Stefan Steinerberger</a>, Mar 24 2006</div> <div class=sectline>From <a href="/wiki/User:Benoit_Cloitre">Benoit Cloitre</a>, Dec 19 2002: (Start)</div> <div class=sectline>a(0) = 0, a(10n+i) = a(n) + i for 0 <= i <= 9.</div> <div class=sectline>a(n) = n - 9*(Sum_{k > 0} floor(n/10^k)) = n - 9*<a href="/A054899" title="a(n) = Sum_{k>0} floor(n/10^k).">A054899</a>(n). (End)</div> <div class=sectline>From <a href="/wiki/User:Hieronymus_Fischer">Hieronymus Fischer</a>, Jun 17 2007: (Start)</div> <div class=sectline>G.f. g(x) = Sum_{k > 0, (x^k - x^(k+10^k) - 9x^(10^k))/(1-x^(10^k))}/(1-x).</div> <div class=sectline>a(n) = n - 9*Sum_{10 <= k <= n} Sum_{j|k, j >= 10} floor(log_10(j)) - floor(log_10(j-1)). (End)</div> <div class=sectline>From <a href="/wiki/User:Hieronymus_Fischer">Hieronymus Fischer</a>, Jun 25 2007: (Start)</div> <div class=sectline>The g.f. can be expressed in terms of a Lambert series, in that g(x) = (x/(1-x) - 9*L[b(k)](x))/(1-x) where L[b(k)](x) = sum{k >= 0, b(k)*x^k/(1-x^k)} is a Lambert series with b(k) = 1, if k > 1 is a power of 10, else b(k) = 0.</div> <div class=sectline>G.f.: g(x) = (Sum_{k > 0} (1 - 9*c(k))*x^k)/(1-x), where c(k) = Sum_{j > 1, j|k} floor(log_10(j)) - floor(log_10(j-1)).</div> <div class=sectline>a(n) = n - 9*Sum_{0 < k <= floor(log_10(n))} a(floor(n/10^k))*10^(k-1). (End)</div> <div class=sectline>From <a href="/wiki/User:Hieronymus_Fischer">Hieronymus Fischer</a>, Oct 06 2007: (Start)</div> <div class=sectline>a(n) <= 9*(1 + floor(log_10(n))), equality holds for n = 10^m - 1, m > 0.</div> <div class=sectline>lim sup (a(n) - 9*log_10(n)) = 0 for n -> oo.</div> <div class=sectline>lim inf (a(n+1) - a(n) + 9*log_10(n)) = 1 for n -> oo. (End)</div> <div class=sectline>a(n) = <a href="/A138530" title="Triangle read by rows: T(n,k) = sum of digits of n in base k representation, 1<=k<=n.">A138530</a>(n, 10) for n > 9. - <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Mar 26 2008</div> <div class=sectline>a(<a href="/A058369" title="Numbers k such that k and k^2 have same digit sum.">A058369</a>(n)) = <a href="/A004159" title="Sum of digits of n^2.">A004159</a>(<a href="/A058369" title="Numbers k such that k and k^2 have same digit sum.">A058369</a>(n)); a(<a href="/A000290" title="The squares: a(n) = n^2.">A000290</a>(n)) = <a href="/A004159" title="Sum of digits of n^2.">A004159</a>(n). - <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Apr 25 2009</div> <div class=sectline>a(n) mod 2 = <a href="/A179081" title="Parity of sum of digits of n.">A179081</a>(n). - <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Jun 28 2010</div> <div class=sectline>a(n) <= 9*log_10(n+1). - <a href="/wiki/User:Vladimir_Shevelev">Vladimir Shevelev</a>, Jun 01 2011</div> <div class=sectline>a(n) = a(n-1) + a(n-10) - a(n-11), for n < 100. - <a href="/wiki/User:Alexander_R._Povolotsky">Alexander R. Povolotsky</a>, Oct 09 2011</div> <div class=sectline>a(n) = Sum_{k >= 0} <a href="/A031298" title="Triangle T(n,k): write n in base 10, reverse order of digits.">A031298</a>(n, k). - <a href="/wiki/User:Philippe_Del茅ham">Philippe Del茅ham</a>, Oct 21 2011</div> <div class=sectline>a(n) = a(n mod b^k) + a(floor(n/b^k)), for all k >= 0. - <a href="/wiki/User:Hieronymus_Fischer">Hieronymus Fischer</a>, Mar 24 2014</div> <div class=sectline>Sum_{n>=1} a(n)/(n*(n+1)) = 10*log(10)/9 (Shallit, 1984). - <a href="/wiki/User:Amiram_Eldar">Amiram Eldar</a>, Jun 03 2021</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>a(123) = 1 + 2 + 3 = 6, a(9875) = 9 + 8 + 7 + 5 = 29.</div> </div> </div> <div class=section> <div class=sectname>MAPLE</div> <div class=sectbody> <div class=sectline><a href="/A007953" title="Digital sum (i.e., sum of digits) of n; also called digsum(n).">A007953</a> := proc(n) add(d, d=convert(n, base, 10)) ; end proc: # <a href="/wiki/User:R._J._Mathar">R. J. Mathar</a>, Mar 17 2011</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Table[Sum[DigitCount[n][[i]] * i, {i, 9}], {n, 50}] (* <a href="/wiki/User:Stefan_Steinerberger">Stefan Steinerberger</a>, Mar 24 2006 *)</div> <div class=sectline>Table[Plus @@ IntegerDigits @ n, {n, 0, 87}] (* or *)</div> <div class=sectline>Nest[Flatten[# /. a_Integer -> Array[a + # &, 10, 0]] &, {0}, 2] (* <a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, Jul 27 2006 *)</div> <div class=sectline>Total/@IntegerDigits[Range[0, 90]] (* <a href="/wiki/User:Harvey_P._Dale">Harvey P. Dale</a>, May 10 2016 *)</div> <div class=sectline>DigitSum[Range[0, 100]] (* Requires v. 14 *) (* <a href="/wiki/User:Paolo_Xausa">Paolo Xausa</a>, May 17 2024 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>/* The next few PARI programs are kept for historical and pedagogical reasons.</div> <div class=sectline> For practical use, the suggested and most efficient code is: <a href="/A007953" title="Digital sum (i.e., sum of digits) of n; also called digsum(n).">A007953</a>=sumdigits */</div> <div class=sectline>(PARI) a(n)=if(n<1, 0, if(n%10, a(n-1)+1, a(n/10))) \\ Recursive, very inefficient. A more efficient recursive variant: a(n)=if(n>9, n=divrem(n, 10); n[2]+a(n[1]), n)</div> <div class=sectline>(PARI) a(n, b=10)={my(s=(n=divrem(n, b))[2]); while(n[1]>=b, s+=(n=divrem(n[1], b))[2]); s+n[1]} \\ <a href="/wiki/User:M._F._Hasler">M. F. Hasler</a>, Mar 22 2011</div> <div class=sectline>(PARI) a(n)=sum(i=1, #n=digits(n), n[i]) \\ Twice as fast. Not so nice but faster:</div> <div class=sectline>(PARI) a(n)=sum(i=1, #n=Vecsmall(Str(n)), n[i])-48*#n \\ - <a href="/wiki/User:M._F._Hasler">M. F. Hasler</a>, May 10 2015</div> <div class=sectline>/* Since PARI 2.7, one can also use: a(n)=vecsum(digits(n)), or better: <a href="/A007953" title="Digital sum (i.e., sum of digits) of n; also called digsum(n).">A007953</a>=sumdigits. [Edited and commented by <a href="/wiki/User:M._F._Hasler">M. F. Hasler</a>, Nov 09 2018] */</div> <div class=sectline>(PARI) a(n) = sumdigits(n); \\ <a href="/wiki/User:Altug_Alkan">Altug Alkan</a>, Apr 19 2018</div> <div class=sectline>(Haskell)</div> <div class=sectline>a007953 n | n < 10 = n</div> <div class=sectline> | otherwise = a007953 n' + r where (n', r) = divMod n 10</div> <div class=sectline>-- <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Nov 04 2011, Mar 19 2011</div> <div class=sectline>(Magma) [ &+Intseq(n): n in [0..87] ]; // <a href="/wiki/User:Bruno_Berselli">Bruno Berselli</a>, May 26 2011</div> <div class=sectline>(Smalltalk)</div> <div class=sectline>"Recursive version for general bases. Set base = 10 for this sequence."</div> <div class=sectline>digitalSum: base</div> <div class=sectline>| s |</div> <div class=sectline>base = 1 ifTrue: [^self].</div> <div class=sectline>(s := self // base) > 0</div> <div class=sectline> ifTrue: [^(s digitalSum: base) + self - (s * base)]</div> <div class=sectline> ifFalse: [^self]</div> <div class=sectline>"by <a href="/wiki/User:Hieronymus_Fischer">Hieronymus Fischer</a>, Mar 24 2014"</div> <div class=sectline>(Python)</div> <div class=sectline>def <a href="/A007953" title="Digital sum (i.e., sum of digits) of n; also called digsum(n).">A007953</a>(n):</div> <div class=sectline> return sum(int(d) for d in str(n)) # <a href="/wiki/User:Chai_Wah_Wu">Chai Wah Wu</a>, Sep 03 2014</div> <div class=sectline>(Python)</div> <div class=sectline>def a(n): return sum(map(int, str(n))) # <a href="/wiki/User:Michael_S._Branicky">Michael S. Branicky</a>, May 22 2021</div> <div class=sectline>(Scala) (0 to 99).map(_.toString.map(_.toInt - 48).sum) // <a href="/wiki/User:Alonso_del_Arte">Alonso del Arte</a>, Sep 15 2019</div> <div class=sectline>(Swift)</div> <div class=sectline><a href="/A007953" title="Digital sum (i.e., sum of digits) of n; also called digsum(n).">A007953</a>(n): String(n).compactMap{$0.wholeNumberValue}.reduce(0, +) // <a href="/wiki/User:Egor_Khmara">Egor Khmara</a>, Jun 15 2021</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A003132" title="Sum of squares of digits of n.">A003132</a>, <a href="/A055012" title="Sum of cubes of the digits of n written in base 10.">A055012</a>, <a href="/A055013" title="Sum of 4th powers of digits of n.">A055013</a>, <a href="/A055014" title="Sum of 5th powers of digits of n.">A055014</a>, <a href="/A055015" title="Sum of 6th powers of digits of n.">A055015</a>, <a href="/A010888" title="Digital root of n (repeatedly add the digits of n until a single digit is reached).">A010888</a>, <a href="/A007954" title="Product of decimal digits of n.">A007954</a>, <a href="/A031347" title="Multiplicative digital root of n (keep multiplying digits of n until reaching a single digit).">A031347</a>, <a href="/A055017" title="Difference between sums of alternate digits of n starting with the last, i.e., (sum of ultimate digit of n, antepenultimate ...">A055017</a>, <a href="/A076313" title="a(n) = floor(n/10) - (n mod 10).">A076313</a>, <a href="/A076314" title="a(n) = floor(n/10) + (n mod 10).">A076314</a>, <a href="/A054899" title="a(n) = Sum_{k>0} floor(n/10^k).">A054899</a>, <a href="/A138470" title="Number of numbers less than n having a smaller sum of digits.">A138470</a>, <a href="/A138471" title="Number of numbers less than n having the same sum of digits.">A138471</a>, <a href="/A138472" title="Number of numbers less than n having a greater sum of digits.">A138472</a>, <a href="/A000120" title="1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).">A000120</a>, <a href="/A004426" title="Arithmetic mean of digits of n (rounded down).">A004426</a>, <a href="/A004427" title="Arithmetic mean of digits of n (rounded up).">A004427</a>, <a href="/A054683" title="Numbers whose sum of digits is even.">A054683</a>, <a href="/A054684" title="Numbers whose sum of digits is odd.">A054684</a>, <a href="/A069877" title="Smallest number with a prime signature whose indices are the decimal digits of n.">A069877</a>, <a href="/A179082" title="Even numbers having an even sum of digits in their decimal representation.">A179082</a>-<a href="/A179085" title="Odd numbers having an odd sum of digits in their decimal representation.">A179085</a>, <a href="/A108971" title="Lexicographically earliest sequence such that in decimal representation sums of digits of consecutive terms differ exactly b...">A108971</a>, <a href="/A169964" title="Numbers whose decimal expansion contains only 0's and 5's.">A169964</a>, <a href="/A179987" title="Digital sums of A108971.">A179987</a>, <a href="/A179988" title="Smallest m such that n = sum of digits of A108971(m).">A179988</a>, <a href="/A180018" title="Difference of sums of digits of n in decimal and in binary representation.">A180018</a>, <a href="/A180019" title="Difference of sums of digits of n in decimal and in ternary representation.">A180019</a>, <a href="/A217928" title="Sum of distinct decimal digits appearing in n.">A217928</a>, <a href="/A216407" title="Sum of decimal digits not appearing in n.">A216407</a>, <a href="/A037123" title="a(n) = a(n-1) + sum of digits of n.">A037123</a>, <a href="/A074784" title="a(n) = a(n-1) + square of the sum of digits of n.">A074784</a>, <a href="/A231688" title="a(n) = Sum_{i=0..n} digsum(i)^3, where digsum(i) = A007953(i).">A231688</a>, <a href="/A231689" title="a(n) = Sum_{i=0..n} digsum(i)^4, where digsum(i) = A007953(i).">A231689</a>, <a href="/A225693" title="Alternating sum of digits of n.">A225693</a>, <a href="/A254524" title="n is the a(n)-th positive integer having its digitsum.">A254524</a> (ordinal transform).</div> <div class=sectline>Bisections: <a href="/A004092" title="Sum of digits of even numbers.">A004092</a>, <a href="/A004155" title="Sum of digits of n-th odd number.">A004155</a>.</div> <div class=sectline>For n + digsum(n) see <a href="/A062028" title="a(n) = n + sum of the digits of n.">A062028</a>.</div> <div class=sectline>Sequence in context: <a href="/A131650" title="Number of symbols in Babylonian numeral representation of n.">A131650</a> <a href="/A033930" title="Base 10 digital convolution sequence.">A033930</a> <a href="/A076314" title="a(n) = floor(n/10) + (n mod 10).">A076314</a> * <a href="/A080463" title="Sum of the two numbers formed by alternate digits of n.">A080463</a> <a href="/A209685" title="Sum of last two digits of n.">A209685</a> <a href="/A114570" title="Let the decimal expansion of n be d_1 d_2 ... d_k; then a(n) = Sum_{i=1..k} d_i^(k+1-i).">A114570</a></div> <div class=sectline>Adjacent sequences: <a href="/A007950" title="Binary sieve: delete every 2nd number, then every 4th, 8th, etc.">A007950</a> <a href="/A007951" title="Ternary sieve: delete every 3rd number, then every 9th, 27th, etc.">A007951</a> <a href="/A007952" title="Generated by a sieve: keep first number, drop every 2nd, keep first, drop every 3rd, keep first, drop every 4th, etc.">A007952</a> * <a href="/A007954" title="Product of decimal digits of n.">A007954</a> <a href="/A007955" title="Product of divisors of n.">A007955</a> <a href="/A007956" title="Product of the proper divisors of n.">A007956</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="a sequence of nonnegative numbers">nonn</span>,<span title="dependent on base used for sequence">base</span>,<span title="an exceptionally nice sequence">nice</span>,<span title="it is very easy to produce terms of sequence">easy</span>,<span title="sequence has an interesting graph"><a href="/A007953/graph">look</a></span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline>R. Muller</div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>More terms from <a href="/wiki/User:Hieronymus_Fischer">Hieronymus Fischer</a>, Jun 17 2007</div> <div class=sectline>Edited by <a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Nov 11 2013</div> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <div class=sectline>approved</div> </div> </div> </div> <div class=space10></div> </div> </div></div> <p> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome"><font color="red">Welcome</font></a> <a href="/wiki/Main_Page"><font color="red">Wiki</font></a> <a href="/wiki/Special:RequestAccount">Register</a> <a href="/play.html">Music</a> <a href="/plot2.html">Plot 2</a> <a href="/demo1.html">Demos</a> <a href="/wiki/Index_to_OEIS">Index</a> <a href="/webcam">WebCam</a> <a href="/Submit.html">Contribute</a> <a href="/eishelp2.html">Format</a> <a href="/wiki/Style_Sheet">Style Sheet</a> <a href="/transforms.html">Transforms</a> <a href="/ol.html">Superseeker</a> <a href="/recent">Recents</a> </div> <div class=linksbar> <a href="/community.html">The OEIS Community</a> </div> <div class=linksbar> Maintained by <a href="http://oeisf.org">The OEIS Foundation Inc.</a> </div> <div class=dbinfo>Last modified November 25 00:47 EST 2024. Contains 378089 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>