OFFSET

0,1

COMMENTS

Numbers that are not in the sequence: 0, 1, 5, 9, 13, 17, 21, 26, 30, 35, 40, 45, 50, 56, 61, 66, 72, 77, 83, 89, 95, 100, 106, 112, 118, 124, 130, 137, 143, 149, 155, 161, 168, ...

It appears that a(n) = A277675(n) + 2 for n >= 1. - Hugo Pfoertner, Jan 27 2021

Sánchez Garza and Treviño proved that the difference between any two consecutive elements is 1 or 2 and that the counting function up to x is x+x/log x + o(x/log x). - Enrique Treviño, Jan 30 2021

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 0..10000

M. Sánchez Garza and E. Treviño, On a sequence related to the factoradic representation of an integer, Journal of Integer Sequences Vol. 24 (2021), Article 21.8.5.

EXAMPLE

Least k>0 such that k! > k^3 is k=6.

For k=5: 5! = 120 < 125 = 5^3.

For k=6: 6! = 720 > 216 = 6^3.

So a(3) = 6.

MATHEMATICA

Table[k = 1; While[k^n >= k!, k++]; k, {n, 0, 100}] (* T. D. Noe, Oct 18 2013 *)

PROG

(Python)

import math

for n in range(333):

for k in range(1, 100000):

if math.factorial(k) > k**n:

print str(k)+', ',

break

(PARI) a(n) = my(k=1); while (k^n >= k!, k++); k; \\ Michel Marcus, Jan 27 2021

CROSSREFS

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Oct 15 2013

STATUS

approved