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

1,1

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

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 *)

Prog

(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

Crossrefs

A090866 is a subsequence.

Cf. A014612, A063639.

Sequence in context: A123840 A258589 A103804 * A092104 A281483 A094105

Adjacent sequences: A063637 A063638 A063639 * A063641 A063642 A063643

Keyword

nonn

Author

Reinhard Zumkeller, Jul 21 2001

Status

approved