A317873 - OEIS

A317873

Number of digits in 2^(n!).

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

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OFFSET

1,3

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 = 1..300

FORMULA

a(n) = A034887(n!).

MAPLE

Digits := 900: # for n <= 300

a := n -> ceil(exp(lnGAMMA(n + 1))*log10(2)):

seq(a(n), n = 1..300); # Peter Luschny, Apr 18 2024

MATHEMATICA

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

CROSSREFS

Cf. A034887, A050923, A055642, A145572.