A262059 - OEIS

%I #16 Aug 01 2019 00:20:03

%S 2,4913,29410,96854,236916,484596,879483,1465239,2289183,3401984,

%T 4857388,6712006,9025131,11858570,15276512,19345406,24133846,29712478,

%U 36153913,43532644,51924974,61408954,72064316,83972419,97216198,111880113,128050105,145813554,165259239,186477301,209559205

%N Least integer k such that k^(1/3)/log(k) exceeds n.

%p A262059val := proc(k)

%p     Digits := 100 ;

%p     evalf(root[3](k)/log(k)) ;

%p end proc:

%p A262059lims := proc(n,lowk,highk)

%p     local vallow, valhigh,midk,valmid ;

%p     vallow := A262059val(lowk) ;

%p     valhigh := A262059val(highk) ;

%p     if valhigh > n and vallow <= n and highk= lowk+1 then

%p         return highk;

%p     else

%p         midk := floor((lowk+highk)/2) ;

%p         valmid := A262059val(midk) ;

%p         if valmid < n then

%p             return procname(n,midk,highk) ;

%p         else

%p             return procname(n,lowk,midk) ;

%p         end if;

%p     end if;

%p end proc:

%p A262059 := proc(n)

%p     local lowk,highk,p ;

%p     if n = 1 then

%p         return 2;

%p     end if;

%p     for p from 0 do

%p         lowk := 10^p ;

%p         highk := 10^(p+1) ;

%p         if A262059val(highk) >=n then

%p             return A262059lims(n,min(2,lowk),highk) ;

%p         end if;

%p     end do:

%p end proc: # _R. J. Mathar_, Oct 22 2015

%t f[n_] := f[n] = Block[{k = f[n - 1]}, While[n > k^(1/3)/Log[k], k++]; k]; f[1] = 2; Array[f, 40]

%o (PARI) a(n) = {my(k = 2); while(sqrtn(k,3)/log(k) <= n, k++); k;} \\ _Michel Marcus_, Sep 10 2015

%Y Cf. A088346, A262058, A262060.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 09 2015