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A224082 The n-th semiprimorial (A112141) minus 1 is prime. 1
1, 2, 6, 7, 11, 17, 20, 21, 36, 69, 84, 168, 207, 248, 401, 431, 435, 1468, 4421 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is the semiprime analogous of A057704.

Search limit: 6000.

LINKS

Table of n, a(n) for n=1..19.

FORMULA

Numbers n such that A112141(n) - 1 is prime.

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

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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Last modified February 18 09:15 EST 2020. Contains 332011 sequences. (Running on oeis4.)