A065801 Least k such that n^k > 2^n.

3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14

Offset

2,1

Links

Harry J. Smith, Table of n, a(n) for n = 2..1000

Example

a(4) = 3 because if k = 2, 4^2 <= 2^4 but when k reaches 3, 4^3 > 2^4.

Mathematica

a[n_] := (k = 1; While[n^k <= 2^n, k++ ]; Return[k]); Table[ a[n], {n, 2, 70} ]
lk[n_]:=Module[{k=Ceiling[Log[n, 2^n]], nt=2^n}, While[n^k<=nt, k++]; k]; Array[ lk, 90, 2] (* Harvey P. Dale, Mar 15 2018 *)

Prog

(PARI) { for (n=2, 1000, k=1; p=2^n; while (n^k <= p, k++); write("b065801.txt", n, " ", k) ) } \\ Harry J. Smith, Oct 31 2009

Crossrefs

Sequence in context: A120004 A079790 A098726 * A265705 A205237 A086920

Adjacent sequences: A065798 A065799 A065800 * A065802 A065803 A065804

Keyword

nonn

Author

Robert G. Wilson v, Dec 05 2001

Extensions

Offset changed from 1 to 2 and Definition corrected by Harry J. Smith, Oct 31 2009

Status

approved