Search: id:A101429
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%I A101429
%S A101429 2,7,115,1366,13561,135178,1351546,13546438,135481777,1354575715
%N A101429 Sum of digits of (2^(10^n)).
%F A101429 a(n)= sum_{m=0..floor(log(2^(10^n)))} floor(10*((2^(10^n))/(10^(((floor(log(2^(10^n)))+1))-m)) 
               - floor ((2^(10^n))/(10^(((floor(log(2^(10^n)))+1))-m))))))
%F A101429 Limit a(n)/10^n, as n -> inf., is 1.35463...=4.5*log(2). For large m, 
               mean value of digits of 2^m is 4.5, according to the uniform probability 
               distribution of digits 0..9 in 2^m. Also, number of decimal digits 
               in 2^m is log(2)*m, hence the formula for limit a(n)/10^n. (Zak Seidov 
               (zakseidov(AT)yahoo Nov 23 2007)
%e A101429 a(4)=sum(m=0,floor(log(2^(10^4))),floor(10*((2^(10^4))/(10^(((floor(log(2^(10^4)))+1))-m)) 
               - floor ((2^(10^4))/(10^(((floor(log(2^(10^4)))+1))-m))))))=13561
%t A101429 f[n_] := Plus @@ IntegerDigits[2^(10^n)]; Table[ f[n], {n, 0, 7}] (from 
               Robert G. Wilson v Nov 05 2004)
%t A101429 f[n_] := Plus @@ IntegerDigits[2^(10^n)]; Table[ f[n], {n, 0, 7}] (from 
               Robert G. Wilson v Nov 05 2004) (* Or *)
%t A101429 g[n_] := Sum[ Floor[10*((2^(10^n))/(10^(((Floor[ Log[10, 2^(10^n)]] + 
               1)) - m)) - Floor[(2^(10^n))/(10^(((Floor[ Log[10, 2^(10^n)]] + 1)) 
               - m))])], {m, 0, Floor[ Log[10, 2^(10^n)]]}]; Table[ g[n], {n, 0, 
               6}]
%Y A101429 Sequence in context: A045310 A000157 A034902 this_sequence A070521 A000889 
               A041727
%Y A101429 Adjacent sequences: A101426 A101427 A101428 this_sequence A101430 A101431 
               A101432
%K A101429 nonn,base
%O A101429 0,1
%A A101429 Yalcin Aktar (aktaryalcin(AT)msn.com), Nov 05 2004
%E A101429 a(5), a(6) & a(7) from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 05 
               2004
%E A101429 a(8) and a(9) from Zak Seidov (zakseidov(AT)yahoo Nov 23 2007

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