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A037123
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a(n) = a(n-1) + Sum of digits of n.
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15
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0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 46, 48, 51, 55, 60, 66, 73, 81, 90, 100, 102, 105, 109, 114, 120, 127, 135, 144, 154, 165, 168, 172, 177, 183, 190, 198, 207, 217, 228, 240, 244, 249, 255, 262, 270, 279, 289, 300, 312, 325, 330, 336, 343, 351, 360, 370, 381
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Sum of digits of A007908(n). - Franz Vrabec (franz.vrabec(AT)aon.at), Oct 22 2007
a(n) = A007953(A053064(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 10 2008]
Also digital sum of A138793(n) for n>0 - Bruno Berselli, May 27 2011
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REFERENCES
| P.-H. Cheo; S.-C. Yien, A problem on the k-adic representation of positive integers. Acta Math. Sinica 5, 433-438 (1955).
H. Riede, Asymptotic estimation of a sum of digits. Fibonacci Q. 36, No. 1, 72-75 (1998).
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LINKS
| Aktar Yalcin, Formula
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FORMULA
| a(n)= Sum_{k=0..n} s(k) = Sum_{k=0..n} A007953(k), where s(k) denote the sum of the digits of k in decimal representation. Asymptotic expression: a(n-1) = Sum_{k=0..n-1} s(k) = 4.5*n*log10(n) + O(n). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002
a(n)=n*(n+1)/2-9*sum(k=1, n, sum(i=1, ceil(log(k)/log(10)), floor(k/10^i))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 28 2003
Contribution from Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 11 2007: (Start)
G.f. g(x)=sum{k>0, (x^k-x^(k+10^k)-9x^(10^k))/(1-x^(10^k))}/(1-x)^2.
a(n)=(1/2)*((n+1)*(n-18*sum{k>0,floor(n/10^k)})+9*sum{k>0,(1+floor(n/10^k= ))*floor(n/10^k)*10^k}).
a(n)=(1/2)*((n+1)*(2*A007953(n)-n)+9*sum{k>0,(1+floor(n/10^k))*floor(n/10^= k)*10^k}). (End)
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PROG
| (PARI) a(n)=n*(n+1)/2-9*sum(k=1, n, sum(i=1, ceil(log(k)/log(10)), floor(k/10^i)))
(Perl) for $i (0..100){ @j = split "", $i; for (@j){ $sum += $_; } print "$sum, "; } __END__ # gamo(AT)telecable.es
(MAGMA) [ n eq 0 select 0 else &+[&+Intseq(k): k in [0..n]]: n in [0..56] ]; // Bruno Berselli, May 27 2011
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CROSSREFS
| Cf. A004207, A016052, A131383, A131384, A131451.
Sequence in context: A061076 A054632 A109453 * A062918 A113168 A071817
Adjacent sequences: A037120 A037121 A037122 * A037124 A037125 A037126
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KEYWORD
| nonn,base,easy
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AUTHOR
| Vasiliy Danilov (danilovv(AT)usa.net) Jun 15 1998
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002
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