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

%I A374665 #11 Jul 16 2024 15:56:21
%S A374665 2,22,222,2223,22232,222222,2222325,22222272,222225552,2222223255,
%T A374665 22222335232,222222327525,2222222372352,22222222575552,
%U A374665 222222223327232,2222222225252352,22222222223327232,222222222272535552,2222222222225252352,22222222222327775232,222222222222737375232
%N A374665 a(n) is the first number that is the concatenation of n primes and also the product of n primes (counted with multiplicity).
%C A374665 Is this a subsequence of A046034?
%F A374665 A001222(a(n)) = n.
%e A374665 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).
%p A374665 f:= proc(n) local k, x, W, L, i;
%p A374665   W:= [2,3,5,7];
%p A374665   for k from 0 to 4^n-1 do
%p A374665     L:= convert(4^n+k,base,4);
%p A374665     x:= add(W[L[i]+1]*10^(i-1),i=1..n);
%p A374665     if numtheory:-bigomega(x) = n then return x fi;
%p A374665   od;
%p A374665 end proc:
%p A374665 map(f, [$1..20]);
%Y A374665 Cf. A001222, A046034. Main diagonal of A374376.
%K A374665 nonn,base
%O A374665 1,1
%A A374665 _Robert Israel_, Jul 15 2024