A071423 a(n) = a(n-1) + number of decimal digits of 2^n. Number of decimal digits of concatenation of first n powers of 2.

1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 34, 39, 44, 49, 55, 61, 67, 74, 81, 88, 95, 103, 111, 119, 128, 137, 146, 156, 166, 176, 186, 197, 208, 219, 231, 243, 255, 268, 281, 294, 307, 321, 335, 349, 364, 379, 394, 410, 426, 442, 458, 475, 492, 509, 527, 545

Offset: 1

Author

Labos Elemer, May 27 2002

Keywords

• easy
• nonn
• base

Crossrefs

Cf. A058183.

Programs

Mathematica

Do[s=s+Length[IntegerDigits[2^n]]; Print[s], {n, 1, 128}]
nxt[{n_,a_}]:={n+1,a+IntegerLength[2^(n+1)]}; NestList[nxt,{1,1},60][[All,2]] (* Harvey P. Dale, Nov 11 2022 *)

Formula

a(n) = a(n-1)+A034887(n). [R. J. Mathar, Sep 11 2009]

a(n) = 0.5 log 2/log 10 * n^2 + O(n)

Extensions

An incorrect g.f. was deleted by N. J. A. Sloane, Sep 13 2009

Formula from Charles R Greathouse IV, Apr 28 2010