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Search: id:A003132
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| A003132 |
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Sum of squares of digits of n.
(Formerly M3355)
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+0
43
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| 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 2, 5, 10, 17, 26, 37, 50, 65, 82, 4, 5, 8, 13, 20, 29, 40, 53, 68, 85, 9, 10, 13, 18, 25, 34, 45, 58, 73, 90, 16, 17, 20, 25, 32, 41, 52, 65, 80, 97, 25, 26, 29, 34, 41, 50, 61, 74, 89, 106, 36, 37, 40, 45, 52, 61, 72, 85, 100, 117, 49
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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It is easy to show that a(n) < 81*(log(n)+1) [log = base 10]. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 25 2006
It is known that a(0)=0 and a(1)=1 are the only fixed points of this map. For more information about iterations of this map, see A099645. [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
B. M. Stewart, Sums of functions of digits, Cand. J. Math., 12 (1960), 374-389.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II
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FORMULA
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a(n)=n^2-20*n*floor(n/10)+81*sum{k>0,floor(n/10^k)^2}+20*sum{k>0,floor(n/10^k)*(floor(n/10^k)-floor(n/10^(k+1)))}. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 17 2007
a(10n+k)=a(n)+k^2, 0<=k<10. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 17 2007
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MAPLE
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for n from 0 to 6 do seq(n^2+j^2, j=0..9 ); od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2006
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MATHEMATICA
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Table[Sum[DigitCount[n][[i]]*i^2, {i, 1, 9}], {n, 1, 40}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 25 2006
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PROGRAM
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(PARI) A003132(n)=norml2(eval(Vec(Str(n)))) \\\\ [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
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CROSSREFS
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Cf. A052034, A052035.
Cf. A007953, A055017, A076313, A076314.
Concerning iterations of this map, see A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), A080709 (starting with 4, this is the only nontrivial limit cycle), A000221 (starting with 5), A008460 (starting with 6), A008462 (starting with 8), A008463 (starting with 9), A139566 (starting with 15), A122065 (starting with 74169). [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
Sequence in context: A063462 A098736 A002015 this_sequence A062331 A069940 A153211
Adjacent sequences: A003129 A003130 A003131 this_sequence A003133 A003134 A003135
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KEYWORD
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nonn,easy,base,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 25 2006
Terms checked using the given PARI code. [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
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