OFFSET
1,3
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000
Michael A. Brilleslyper, Nathan Wakefield, A. J. Wallerstein, and Bradley Warner, Comparing the Growth of the Prime Numbers to the Natural Numbers, Fibonacci Quart. 54 (2016), no. 1, 65-71.
FORMULA
a(n) = f(n) + 1, where f(n) is the function defined on p. 65 of Brilleslyper et al. - Michel Marcus, Apr 11 2022
MATHEMATICA
lk[n_]:=Module[{k=1, f=n!}, While[f>=Times@@Table[n+i, {i, k}], k++]; k]; Array[lk, 80] (* Harvey P. Dale, Sep 20 2016 *)
PROG
(PARI) a(n) = my(k=0); while (n!^2 >= (n+k)!, k++); k; \\ Michel Marcus, Apr 11 2022
(Python)
from math import factorial
def a(n):
fn, k, p = factorial(n), 1, n+1
while fn >= p: k += 1; p *= (n+k)
return k
print([a(n) for n in range(1, 75)]) # Michael S. Branicky, Apr 11 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, May 15 2004
EXTENSIONS
Corrected and extended by Ray Chandler, May 23 2004
STATUS
approved