0,3

Sum of digits of A007908(n). - Franz Vrabec (franz.vrabec(AT)planetuniqa.at), Oct 22 2007

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).

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

G.f. g(x)=sum{k>0, (x^k-x^(k+10^k)-9x^(10^k))/(1-x^(10^k))}/(1-x)^2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 11 2007

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}). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 11 2007

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}). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 11 2007

(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) #!/usr/local/bin/perl -w for $i (0..100){ @j = split "", $i; for (@j){ $sum += $_; } print "$sum, "; } __END__ (gamo(AT)telecable.es)

Cf. A004207, A016052.

Cf. A131383, A131384, A131451.

Sequence in context: A061076 A054632 A109453 this_sequence A062918 A113168 A071817

Adjacent sequences: A037120 A037121 A037122 this_sequence A037124 A037125 A037126

nonn,base

Vasiliy Danilov (danilovv(AT)usa.net) Jun 15 1998

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002