A063640 Primes of form p*q*r + 1, where p, q and r are primes.

13, 19, 29, 31, 43, 53, 67, 71, 79, 103, 131, 139, 149, 173, 191, 223, 239, 269, 283, 293, 311, 317, 367, 389, 419, 431, 439, 443, 499, 509, 557, 599, 607, 619, 643, 647, 653, 659, 683, 743, 773, 787, 797, 823, 827, 907, 947, 971, 1031, 1039, 1087, 1091

Offset: 1

Author

Reinhard Zumkeller, Jul 21 2001

Keywords

• nonn

Comments

Odd primes p such that (p-1)/2 is a semiprime. - Robert G. Wilson v, Sep 01 2007

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

A090866 is a subsequence.

Cf. A014612, A063639.

Programs

Maple

q:= n-> isprime(n) and numtheory[bigomega](n-1)=3:
select(q, [$2..1100])[];  # Alois P. Heinz, Mar 08 2023

Mathematica

Take[ Select[ Union@ Flatten@ Table[ Prime@p*Prime@q*Prime@r + 1, {p, 48}, {q, p}, {r, q}], PrimeQ@ # &], 53] (* Or *)
semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger[x] == 2; Select[Prime@ Range@ 182, semiPrimeQ[(# - 1)/2] &] (* Robert G. Wilson v, Sep 01 2007 *)
2#+1&/@Select[Table[(n-1)/2,{n,Prime[Range[200]]}],PrimeOmega[#]==2&] (* Harvey P. Dale, Oct 11 2018 *)

PARI

n=0; for (m=1, 10^9, p=prime(m); if (bigomega(p - 1) == 3, write("b063640.txt", n++, " ", p); if (n==1000, break)) )  \\ Harry J. Smith, Aug 26 2009