This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086824 #28 Mar 07 2024 08:43:20
%S A086824 1,1,4,7,9,12,14,17,20,22,25,28,30,33,36,38,41,44,47,49,52,55,57,60,
%T A086824 63,65,68,71,73,76,79,82,84,87,90,92,95,98,101,103,106,109,111,114,
%U A086824 117,119,122,125,128,130,133,136,138,141,144,147,149,152,155,157,160,163,166
%N A086824 Least positive k such that k! >= n^k.
%C A086824 Suggested by Richard-Andre Jeannin (andre-jeannin.richard(AT)wanadoo.fr).
%H A086824 Alois P. Heinz, <a href="/A086824/b086824.txt">Table of n, a(n) for n = 0..10000</a>
%F A086824 a(n) = e*n + O(log(n)); a(n+1)-a(n) = 2 or 3.
%F A086824 Conjecture: for n>3 a(n) = round(e*n-(1/2)*log(2*Pi*n)-1/n). - _Benoit Cloitre_, Dec 14 2005
%F A086824 Above conjecture is false: For n = 195 we have: a(n) = 526 < 527 = round(exp(1)*n -(1/2)*log(2*Pi*n)-1/n). - _Alois P. Heinz_, Jan 15 2022
%p A086824 a:= proc(n) option remember; local k; if n<0 then 1 else
%p A086824 for k from a(n-1) while k! < n^k do od; k fi
%p A086824 end:
%p A086824 seq(a(n), n=0..80); # _Alois P. Heinz_, Jan 15 2022
%t A086824 f[n_] := Block[{k = 1}, While[k! < n^k, k++ ]; k]; Table[ f[n], {n, 62}] (* _Robert G. Wilson v_, Jun 12 2004 *)
%o A086824 (PARI) a(n)=if(n<2,1,k=1; while(k!<n^k,k++); k)
%Y A086824 Variant of A065027. - _R. J. Mathar_, Sep 12 2008
%K A086824 nonn
%O A086824 0,3
%A A086824 _Benoit Cloitre_, Aug 07 2003
%E A086824 Missing a(0)=1 inserted by _Alois P. Heinz_, Jan 15 2022