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Numbers k such that A112141(k) + 1 is prime.
1

%I #30 Feb 12 2023 14:25:03

%S 1,4,5,6,11,12,18,39,51,98,124,170,179,208,248,838,919,939,1233,1352,

%T 2177,3070,10714

%N Numbers k such that A112141(k) + 1 is prime.

%C This is the semiprime analog to A014545.

%e 4*6*9*10+1 = 2161 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 < 4651, If[ PrimeQ[f[k] + 1], Print[k]; AppendTo[lst, k]]; k++]; lst

%Y Cf. A112141, A014545, A224082.

%K nonn,more

%O 1,2

%A _Jonathan Vos Post_ and _Robert G. Wilson v_, Apr 02 2013

%E a(23) from _Tyler Busby_, Feb 12 2023