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.

2, 22, 222, 2223, 22232, 222222, 2222325, 22222272, 222225552, 2222223255, 22222335232, 222222327525, 2222222372352, 22222222575552, 222222223327232, 2222222225252352, 22222222223327232, 222222222272535552, 2222222222225252352, 22222222222327775232, 222222222222737375232, 2222222222227572375552

Offset: 1

Author

Robert Israel, May 27 2025

Keywords

• nonn
• base

Comments

How is this related to A374665? - R. J. Mathar, May 30 2025

Examples

			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.
		

Programs

Maple

PD:= [2,3,5,7]:
f:= proc(n) local x,L,t,i;
    for x from 4^n to 2*4^n-1 do
      L:= convert(x,base,4);
      t:= add(PD[L[i]+1]*10^(i-1),i=1..n);
      if numtheory:-bigomega(t) = n then return t fi
    od;
    -1
end proc;
map(f, [$1..25]);