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a(n) is the first number that is the concatenation of n primes and also the product of n primes (counted with multiplicity).
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%I #11 Jul 16 2024 15:56:21

%S 2,22,222,2223,22232,222222,2222325,22222272,222225552,2222223255,

%T 22222335232,222222327525,2222222372352,22222222575552,

%U 222222223327232,2222222225252352,22222222223327232,222222222272535552,2222222222225252352,22222222222327775232,222222222222737375232

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

%C Is this a subsequence of A046034?

%F A001222(a(n)) = n.

%e 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 f:= proc(n) local k, x, W, L, i;

%p W:= [2,3,5,7];

%p for k from 0 to 4^n-1 do

%p L:= convert(4^n+k,base,4);

%p x:= add(W[L[i]+1]*10^(i-1),i=1..n);

%p if numtheory:-bigomega(x) = n then return x fi;

%p od;

%p end proc:

%p map(f, [$1..20]);

%Y Cf. A001222, A046034. Main diagonal of A374376.

%K nonn,base

%O 1,1

%A _Robert Israel_, Jul 15 2024