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 A224082 Numbers k such that A112141(k) - 1 is prime. 1
 1, 2, 6, 7, 11, 17, 20, 21, 36, 69, 84, 168, 207, 248, 401, 431, 435, 1468, 4421, 8949 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is the semiprime analog of A057704. a(21) > 10000. - Tyler Busby, Feb 12 2023 LINKS 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

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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)