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Search: id:A074784
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| A074784 |
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a(n) = a(n-1) + square of the sum of digits of n. |
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+0
1
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| 1, 5, 14, 30, 55, 91, 140, 204, 285, 286, 290, 299, 315, 340, 376, 425, 489, 570, 670, 674, 683, 699, 724, 760, 809, 873, 954, 1054, 1175, 1184, 1200, 1225, 1261, 1310, 1374, 1455, 1555, 1676, 1820, 1836, 1861, 1897, 1946, 2010, 2091, 2191, 2312, 2456
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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R. E. Kennedy and C. N. Cooper, An extension of a theorem by Cheo and Yien concerning digital sums. Fibonacci Q. 29, No. 2, 145-149 (1991).
H. Riede, Asymptotic estimation of a sum of digits. Fibonacci Q. 36, No. 1, 72-75 (1998).
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FORMULA
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a(n)= Sum_{k=1..n} s(k)^2 = Sum_{k=1..n} A007953(k)^2, where s(k) denote the sum of the digits of k in decimal representation. Asymptotic expression: a(n-1) = Sum_{k=1..n-1} s(k)^2 = 20.25*n*log10(n)^2 + O(n*log10(n)) . In general: Sum_{k=1..n-1} s(k)^m = n*((9/2)*log10(n))^m + O(n*log10(n)^(m-1)).
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CROSSREFS
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Cf. A037123.
Sequence in context: A053461 A136135 A096893 this_sequence A109678 A000330 A166068
Adjacent sequences: A074781 A074782 A074783 this_sequence A074785 A074786 A074787
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KEYWORD
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nonn,base
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AUTHOR
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Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002
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