A075357 a(n) = smallest k such that (n+1)(n+2)...(n+k) >= n!.

0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 52, 53, 53, 54

Offset: 1

Author

Amarnath Murthy, Sep 19 2002

Keywords

• nonn

Comments

Is this sequence the same as A094331? - David Wasserman, Jan 16 2005

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A075358.

Cf. A094331.

Programs

PARI

a(n) = my(k=0); while ((n+k)! < n!^2, k++); k; \\ Michel Marcus, Apr 11 2022

Python

from math import factorial
def a(n):
    if n == 1: return 0
    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

Extensions

More terms from David Wasserman, Jan 16 2005