OFFSET
1,2
COMMENTS
Also, the least m>0 such that n! < L(m), where L = A000032, the Lucas numbers.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
Aleksandar Petojević, Lambert's W function and Kurepa's left factorial, Project: Kurepa's hypothesis for left factorial, ResearchGate (2023).
Aleksandar Petojević, Marjana Gorjanac Ranitović, Dragan Rastovac, and Milinko Mandić, The Golden Ratio, Factorials, and the Lambert W Function, Journal of Integer Sequences, Vol. 27 (2024), Article 24.5.7.
EXAMPLE
a(4) = 7 because r^6 < 4! <= 4^7.
MATHEMATICA
Table[m=1; While[n!>GoldenRatio^m, m++]; m, {n, 1, 100}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 18 2012
STATUS
approved