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%I #11 Jun 17 2018 02:01:23
%S 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,
%T 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,
%U 11,11,11,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,14,14,14,14,14
%N Least k such that n^k > 2^n.
%H Harry J. Smith, <a href="/A065801/b065801.txt">Table of n, a(n) for n = 2..1000</a>
%e a(4) = 3 because if k = 2, 4^2 <= 2^4 but when k reaches 3, 4^3 > 2^4.
%t a[n_] := (k = 1; While[n^k <= 2^n, k++ ]; Return[k]); Table[ a[n], {n, 2, 70} ]
%t 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 *)
%o (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
%K nonn
%O 2,1
%A _Robert G. Wilson v_, Dec 05 2001
%E Offset changed from 1 to 2 and Definition corrected by _Harry J. Smith_, Oct 31 2009
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