A108141 Least k such that the number (n+1)(n+2)(n+3)...(n+k) >= n^n.

1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Maple

a:=proc(n) local S, k: S:={}: for k from 1 to n do if product(n+i, i=1..k)>n^n then S:=S union {k} else S:=S fi: od; S[1]: end: seq(a(n), n=1..81); # Emeric Deutsch, Aug 03 2005

Mathematica

lk[n_]:=Module[{k=1, c=n^n}, While[Times@@Range[n+1, n+k]<c, k++]; k]; Array[ lk, 80] (* Harvey P. Dale, Dec 31 2022 *)

Crossrefs

Cf. A108135.

Sequence in context: A332613 A072932 A029915 * A291811 A291812 A363694

Adjacent sequences: A108138 A108139 A108140 * A108142 A108143 A108144

Keyword

nonn

Author

Amarnath Murthy, Jul 23 2005

Extensions

More terms from Emeric Deutsch, Aug 03 2005

Status

approved