A224082 Numbers k such that A112141(k) - 1 is prime.

1, 2, 6, 7, 11, 17, 20, 21, 36, 69, 84, 168, 207, 248, 401, 431, 435, 1468, 4421, 8949

Offset

1,2

Comments

This is the semiprime analog of A057704.

a(21) > 10000. - Tyler Busby, Feb 12 2023

Links

Table of n, a(n) for n=1..20.

Example

4*6*9*10*14*15 - 1 = 453599 which is prime.

Mathematica

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

Prog

(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

Crossrefs

Cf. A112141, A057704, A224081.

Sequence in context: A231500 A174000 A241720 * A051678 A079906 A226814

Adjacent sequences: A224079 A224080 A224081 * A224083 A224084 A224085

Keyword

nonn,more

Author

Jonathan Vos Post and Robert G. Wilson v, Apr 02 2013

Extensions

a(19) from Charles R Greathouse IV, Apr 03 2013

a(20) from Tyler Busby, Feb 12 2023

Status

approved