A317873 Number of digits in 2^(n!).

1, 1, 1, 2, 8, 37, 217, 1518, 12138, 109238, 1092378, 12016155, 144193850, 1874520045, 26243280622, 393649209329, 6298387349264, 107072584937472, 1927306528874488, 36618824048615255, 732376480972305082, 15379906100418406713, 338357934209204947674

Offset: 0

Author

Wolfdieter Lang and Robert G. Wilson v, Aug 09 2018

Keywords

• nonn
• base

Comments

The old definition (which did not match the data) was "Number of digits in the numerators of partial sums for Liouville's constant, read as base-2 (binary) numbers (A145572)."

Links

• Kevin Ryde, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000142, A034887, A050923, A055642, A145572.

Programs

Maple

Digits := 900: # for n <= 300
a := n -> ceil(exp(lnGAMMA(n + 1))*log10(2)):
seq(a(n), n = 0..30);  # Peter Luschny, Apr 18 2024

Mathematica

Array[ Floor[#! Log10@2 + 1] &, 22]

Formula

a(n) = A034887(n!).

Extensions

Better definition suggested by Martin Renner, Mar 24 2024

a(0)=1 prepended by Alois P. Heinz, Jul 27 2025