Search: id:A074784
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%I A074784
%S A074784 1,5,14,30,55,91,140,204,285,286,290,299,315,340,376,425,489,570,670,
%T A074784 674,683,699,724,760,809,873,954,1054,1175,1184,1200,1225,1261,1310,
%U A074784 1374,1455,1555,1676,1820,1836,1861,1897,1946,2010,2091,2191,2312,2456
%N A074784 a(n) = a(n-1) + square of the sum of digits of n.
%D A074784 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).
%D A074784 H. Riede, Asymptotic estimation of a sum of digits. Fibonacci Q. 36, 
               No. 1, 72-75 (1998).
%F A074784 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)).
%Y A074784 Cf. A037123.
%Y A074784 Sequence in context: A053461 A136135 A096893 this_sequence A109678 A000330 
               A166068
%Y A074784 Adjacent sequences: A074781 A074782 A074783 this_sequence A074785 A074786 
               A074787
%K A074784 nonn,base
%O A074784 1,2
%A A074784 Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002

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