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A384403 a(n) is the smallest number with n digits, all of which are prime, and n prime factors, counted with multiplicity, or -1 if there is no such number.

%I A384403 #8 Jun 02 2025 12:59:18
%S A384403 2,22,222,2223,22232,222222,2222325,22222272,222225552,2222223255,
%T A384403 22222335232,222222327525,2222222372352,22222222575552,
%U A384403 222222223327232,2222222225252352,22222222223327232,222222222272535552,2222222222225252352,22222222222327775232,222222222222737375232,2222222222227572375552
%N A384403 a(n) is the smallest number with n digits, all of which are prime, and n prime factors, counted with multiplicity, or -1 if there is no such number.
%C A384403 How is this related to A374665? - _R. J. Mathar_, May 30 2025
%e A384403 a(4) = 2223 because the four digits 2,2,2,3 are prime and 2223 = 3^2 * 13 * 19 has 4 prime factors, counted with multiplicity.
%p A384403 PD:= [2,3,5,7]:
%p A384403 f:= proc(n) local x,L,t,i;
%p A384403     for x from 4^n to 2*4^n-1 do
%p A384403       L:= convert(x,base,4);
%p A384403       t:= add(PD[L[i]+1]*10^(i-1),i=1..n);
%p A384403       if numtheory:-bigomega(t) = n then return t fi
%p A384403     od;
%p A384403     -1
%p A384403 end proc;
%p A384403 map(f, [$1..25]);
%K A384403 nonn,base
%O A384403 1,1
%A A384403 _Robert Israel_, May 27 2025