A374665 a(n) is the first number that is the concatenation of n primes and also the product of n primes (counted with multiplicity).

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

Offset: 1

Author

Robert Israel, Jul 15 2024

Keywords

• nonn
• base

Comments

Is this a subsequence of A046034?

Examples

			a(5) = 22232 because 22232 is the concatenation of the 5 primes 2, 2, 2, 3, 2 and 22232 = 2^3 * 7 * 397 is the product of 5 primes (counted with multiplicity).
		

Crossrefs

Cf. A001222, A046034. Main diagonal of A374376.

Programs

Maple

f:= proc(n) local k, x, W, L, i;
  W:= [2,3,5,7];
  for k from 0 to 4^n-1 do
    L:= convert(4^n+k,base,4);
    x:= add(W[L[i]+1]*10^(i-1),i=1..n);
    if numtheory:-bigomega(x) = n then return x fi;
  od;
end proc:
map(f, [$1..20]);

Formula

A001222(a(n)) = n.