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

1,2

Links

Table of n, a(n) for n=1..58.

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)

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 *)

Crossrefs

Cf. A058183.

Sequence in context: A279984 A184017 A024195 * A211004 A062781 A145919

Adjacent sequences: A071420 A071421 A071422 * A071424 A071425 A071426

Keyword

easy,nonn,base

Author

Labos Elemer, May 27 2002

Extensions

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

Formula from Charles R Greathouse IV, Apr 28 2010

Status

approved