login
A076946
Smallest k such that n*(n+1)*(n+2)...*(n+k) >= n^n.
1
0, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67
OFFSET
1,3
COMMENTS
Limit_{n -> oo} a(n)/n = 1. [edited by Robert Israel, Nov 09 2022]
LINKS
FORMULA
a(n) ~ n. - Charles R Greathouse IV, Nov 17 2022
EXAMPLE
a(3) = 2 as 3*4*5 > 3^3. but 3*4 < 3^3.
MAPLE
f:= proc(n) local k, s, t;
t:= n^n;
s:= 1;
for k from 0 do
s:= s*(n+k);
if s >= t then return k fi
od;
end proc:
map(f, [$1..100]); # Robert Israel, Nov 09 2022
MATHEMATICA
a[n_] := Module[{k, nn = n^n, p = 1}, For[k = 0, True, k++, p = p(n+k); If[p >= nn, Return[k]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, May 23 2023 *)
PROG
(PARI) a(n) = my(x=n^n, p=1); for (k=0, oo, p*=(n+k); if (p>=x, return(k))); \\ Michel Marcus, Nov 17 2022
CROSSREFS
Sequence in context: A172475 A171970 A071377 * A302780 A064524 A153249
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Oct 20 2002
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Oct 21 2002
STATUS
approved