A244061 The number of digits of (2^n)!.

1, 1, 2, 5, 14, 36, 90, 216, 507, 1167, 2640, 5895, 13020, 28504, 61937, 133734, 287194, 613842, 1306594, 2771010, 5857670, 12346641, 25955890, 54436999, 113924438, 237949763, 496101303, 1032606162, 2146019444, 4453653132, 9230534755

Offset: 0

Author

Robert G. Wilson v, Jun 18 2014

Keywords

• nonn
• base

Crossrefs

Cf. A000722, A061010, A244060.

Programs

Mathematica

LogBase10Stirling[n_] := Floor[ Log[10, 2 Pi n]/2 + n*Log[10, n/E] + Log[10, 1 + 1/(12 n) + 1/(288 n^2) - 139/(51840 n^3) - 571/(2488320 n^4) + 163879/(209018880 n^5)]]; Table[ LogBase10Stirling[2^n] + 1, {n, 0, 30}]
IntegerLength[(2^Range[0,30])!] (* Harvey P. Dale, Nov 05 2021 *)