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%I #11 Nov 11 2022 15:08:58
%S 1,2,3,5,7,9,12,15,18,22,26,30,34,39,44,49,55,61,67,74,81,88,95,103,
%T 111,119,128,137,146,156,166,176,186,197,208,219,231,243,255,268,281,
%U 294,307,321,335,349,364,379,394,410,426,442,458,475,492,509,527,545
%N a(n) = a(n-1) + number of decimal digits of 2^n. Number of decimal digits of concatenation of first n powers of 2.
%F a(n) = a(n-1)+A034887(n). [_R. J. Mathar_, Sep 11 2009]
%F a(n) = 0.5 log 2/log 10 * n^2 + O(n)
%t Do[s=s+Length[IntegerDigits[2^n]]; Print[s], {n, 1, 128}]
%t nxt[{n_,a_}]:={n+1,a+IntegerLength[2^(n+1)]}; NestList[nxt,{1,1},60][[All,2]] (* _Harvey P. Dale_, Nov 11 2022 *)
%Y Cf. A058183.
%K easy,nonn,base
%O 1,2
%A _Labos Elemer_, May 27 2002
%E An incorrect g.f. was deleted by _N. J. A. Sloane_, Sep 13 2009
%E Formula from _Charles R Greathouse IV_, Apr 28 2010
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