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%I #34 Feb 12 2023 14:25:14
%S 1,2,6,7,11,17,20,21,36,69,84,168,207,248,401,431,435,1468,4421,8949
%N Numbers k such that A112141(k) - 1 is prime.
%C This is the semiprime analog of A057704.
%C a(21) > 10000. - _Tyler Busby_, Feb 12 2023
%e 4*6*9*10*14*15 - 1 = 453599 which is prime.
%t NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[ PrimeOmega[sp] != 2, If[sgn < 0, sp--, sp++]]; If[sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]]; f[n_] := Times @@ NestList[NextSemiPrime, 2^2, n - 1]; k = 1; lst = {}; While[k < 3501, If[ PrimeQ[f[k] - 1], Print[k]; AppendTo[lst, k]]; k++]; lst
%o (PARI) s=3;t=1;for(n=1,1000,while(bigomega(s++)!=2,);t*=s;if(ispseudoprime(t-1),print1(n", "))) \\ _Charles R Greathouse IV_, Apr 03 2013
%Y Cf. A112141, A057704, A224081.
%K nonn,more
%O 1,2
%A _Jonathan Vos Post_ and _Robert G. Wilson v_, Apr 02 2013
%E a(19) from _Charles R Greathouse IV_, Apr 03 2013
%E a(20) from _Tyler Busby_, Feb 12 2023