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A262058 Least integer k>1 such that sqrt(k)/log(k) exceeds n.

%I A262058 #21 Oct 23 2015 03:56:24
%S A262058 2,2,289,681,1280,2109,3190,4538,6170,8100,10339,12901,15795,19032,
%T A262058 22620,26570,30888,35583,40662,46133,52003,58277,64962,72065,79590,
%U A262058 87544,95932,104759,114030,123750,133924,144557,155652,167215,179250,191760
%N A262058 Least integer k>1 such that sqrt(k)/log(k) exceeds n.
%H A262058 Danny Rorabaugh, <a href="/A262058/b262058.txt">Table of n, a(n) for n = 1..10000</a>
%p A262058 A262058 := proc(n)
%p A262058     Digits := 30 ;
%p A262058     for k from 2 do
%p A262058         if evalf(sqrt(k) > n*log(k)) then
%p A262058             return k;
%p A262058         end if;
%p A262058     end do:
%p A262058 end proc: # _R. J. Mathar_, Oct 22 2015
%t A262058 f[n_] := f[n] = Block[{k = f[n - 1]}, While[n > Sqrt[k]/Log[k], k++]; k]; f[1] = 2; Array[f, 50]
%o A262058 (PARI) a(n) = {my(k = 2); while(sqrt(k)/log(k) <= n, k++); k;} \\ _Michel Marcus_, Sep 10 2015
%o A262058 (Sage)
%o A262058 def A262058(n,d=50):
%o A262058     (low,high) = (1,2)
%o A262058     while N(sqrt(high),digits=d) <= N(n*log(high),digits=d):
%o A262058         high *= 2
%o A262058     while low+1<high:
%o A262058         mid = ceil((low+high)/2)
%o A262058         if N(sqrt(mid),digits=d) <= N(n*log(mid),digits=d):
%o A262058             low = mid
%o A262058         else:
%o A262058             high = mid
%o A262058     return high # _Danny Rorabaugh_, Sep 26 2015
%Y A262058 Cf. A088346, A262059, A262060.
%K A262058 nonn
%O A262058 1,1
%A A262058 _Robert G. Wilson v_, Sep 09 2015