login
Least positive number k such that k^k is at least 10^n digits long.
0

%I #25 Nov 30 2019 01:32:14

%S 1,10,57,387,2890,22934,189482,1611056,13993960,123579654,1105747503,

%T 10000000000,91239358932,838673386122,7758099162327,72158973089377,

%U 674359248152535,6328590417713813,59611349660814244,563355446524384647,5339735395113038337

%N Least positive number k such that k^k is at least 10^n digits long.

%F a(n) = ceiling(exp(W(10^n*log(10)))) for n > 0. - _Charles R Greathouse IV_, Nov 16 2014

%o (PARI) a(n)= k=floor(sqrt(10^n));while(#digits(k^k)<10^n,k++);k

%o n=0;while(n<10,print1(a(n),", ");n++)

%o (PARI) a(n)=if(n, ceil(exp(lambertw(10^n*log(10)))), 1) \\ _Charles R Greathouse IV_, Nov 16 2014

%K nonn,base

%O 0,2

%A _Derek Orr_, Nov 15 2014

%E More terms from _Alois P. Heinz_, Nov 15 2014