cp's OEIS Frontend

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

%I A075357 #9 Apr 11 2022 15:28:05
%S A075357 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,
%T A075357 19,20,21,21,22,23,24,24,25,26,27,27,28,29,30,30,31,32,33,33,34,35,36,
%U A075357 37,37,38,39,40,40,41,42,43,43,44,45,46,47,47,48,49,50,50,51,52,53,53,54
%N A075357 a(n) = smallest k such that (n+1)(n+2)...(n+k) >= n!.
%C A075357 Is this sequence the same as A094331? - _David Wasserman_, Jan 16 2005
%H A075357 Michael S. Branicky, <a href="/A075357/b075357.txt">Table of n, a(n) for n = 1..10000</a>
%o A075357 (PARI) a(n) = my(k=0); while ((n+k)! < n!^2, k++); k; \\ _Michel Marcus_, Apr 11 2022
%o A075357 (Python)
%o A075357 from math import factorial
%o A075357 def a(n):
%o A075357     if n == 1: return 0
%o A075357     fn, k, p = factorial(n), 1, n+1
%o A075357     while fn > p: k += 1; p *= (n+k)
%o A075357     return k
%o A075357 print([a(n) for n in range(1, 75)]) # _Michael S. Branicky_, Apr 11 2022
%Y A075357 Cf. A075358.
%Y A075357 Cf. A094331.
%K A075357 nonn
%O A075357 1,3
%A A075357 _Amarnath Murthy_, Sep 19 2002
%E A075357 More terms from _David Wasserman_, Jan 16 2005