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A373656 a(n) is the n-th prime after the n-th semiprime.

%I A373656 #29 Jul 07 2024 20:52:47
%S A373656 5,11,17,19,31,37,47,53,61,67,79,83,89,101,103,113,131,137,149,151,
%T A373656 157,173,179,191,199,211,227,233,239,241,257,263,269,271,293,313,331,
%U A373656 337,347,349,353,359,373,383,389,409,419,421,431,433,449,461,463,467,487,499,509,521,547,557,563,577
%N A373656 a(n) is the n-th prime after the n-th semiprime.
%H A373656 Robert Israel, <a href="/A373656/b373656.txt">Table of n, a(n) for n = 1..10000</a>
%F A373656 a(n) = A000040(n + A000720(A001358(n))).
%e A373656 a(5) = 31 because the 5th semiprime is 14 and the first 5 primes after 14 are 17, 19, 23, 29, 31.
%p A373656 N:= 1000: # for terms <= N
%p A373656 P:= select(isprime, [2, seq(i, i=3..N, 2)]): nP:= nops(P):
%p A373656 S:= select(t -> numtheory:-bigomega(t)=2, [$1..N]):
%p A373656 f:= proc(n) local j;
%p A373656   j:= ListTools:-BinaryPlace(P, S[n]);
%p A373656   if j + n <= nP then P[j+n] else fail fi
%p A373656 end proc:
%p A373656 R:= NULL:
%p A373656 for i from 1 do
%p A373656   v:= f(i);
%p A373656   if v = fail then break fi;
%p A373656   R:= R, v
%p A373656 od:
%p A373656 R;
%t A373656 sp=Select[Range[200],PrimeOmega[#]==2&];Table[NextPrime[sp[[n]],n],{n,62}] (* _James C. McMahon_, Jul 07 2024 *)
%Y A373656 Cf. A000040, A000720, A001358, A373630.
%K A373656 nonn
%O A373656 1,1
%A A373656 _Zak Seidov_ and _Robert Israel_, Jun 14 2024