A356585 Number of decimal digits in the n-th Gosper hyperfactorial of n (A330716).

1, 1, 2, 16, 198, 2927, 50060, 979361, 21645853, 534381060, 14590180163, 436814197446, 14235563000269, 501817445873045, 19029286646922723, 772532087068933899, 33434018751249535666, 1536767964161539414904, 74769012084248550773909

Offset

0,3

Comments

The 0th Gosper hyperfactorial is the usual factorial function.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = A055642(A330716(n)).

Example

a(0)=1 since the 0th Gosper hyperfactorial (0!) has one decimal digit.
a(3)=16 since the 3rd Gosper hyperfactorial of 3 is 1952152956156672.

Mathematica

Floor[Table[1+Sum[Log10[k]*(k^n), {k, 1, n}], {n, 1, 18}]]

Prog

(PARI) a(n) = floor(sum(k=1, n, log(k)*k^n/log(10))) + 1; \\ Michel Marcus, Sep 27 2022

Crossrefs

Cf. A055642, A330716, A356586.

Sequence in context: A274448 A209586 A334237 * A012683 A012677 A158212

Adjacent sequences: A356582 A356583 A356584 * A356586 A356587 A356588

Keyword

nonn,base

Author

Greg Huber, Aug 13 2022

Status

approved