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A345073 a(n) is the least integer k such that e * (n!)^(1/n) < n + k. 2
2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..1000

David E. Radford, Factorials and powers, a minimality result, arXiv:2106.02002 [math.NT], 2021.

David E. Radford, Factorials and powers, a minimality result, revisited, arXiv:2106.02109 [math.NT], 2021.

PROG

(PARI) a(n) = my(k=1); while (exp(1)*sqrtn(n!, n) >= n+k, k++); k;

CROSSREFS

Cf. A001113 (e), A345074.

Sequence in context: A230516 A192688 A156752 * A086673 A101787 A343607

Adjacent sequences:  A345070 A345071 A345072 * A345074 A345075 A345076

KEYWORD

nonn

AUTHOR

Michel Marcus, Jun 07 2021

STATUS

approved

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)