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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
29
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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
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REFERENCES
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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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CROSSREFS
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Cf. A052034, A052035.
Cf. A007953, A055017, A076313, A076314.
Adjacent sequences: A003129 A003130 A003131 this_sequence A003133 A003134 A003135
Sequence in context: A063462 A098736 A002015 this_sequence A062331 A069940 A118881
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KEYWORD
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nonn,easy,base,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 25 2006
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