

A075357


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


3



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
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OFFSET

1,3


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


PROG

(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


CROSSREFS

Cf. A075358.
Cf. A094331.
Sequence in context: A038372 A121930 A020909 * A094331 A135672 A265133
Adjacent sequences: A075354 A075355 A075356 * A075358 A075359 A075360


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Sep 19 2002


EXTENSIONS

More terms from David Wasserman, Jan 16 2005


STATUS

approved



