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%I #24 Mar 08 2023 14:59:29
%S 13,19,29,31,43,53,67,71,79,103,131,139,149,173,191,223,239,269,283,
%T 293,311,317,367,389,419,431,439,443,499,509,557,599,607,619,643,647,
%U 653,659,683,743,773,787,797,823,827,907,947,971,1031,1039,1087,1091
%N Primes of form p*q*r + 1, where p, q and r are primes.
%C Odd primes p such that (p-1)/2 is a semiprime. - _Robert G. Wilson v_, Sep 01 2007
%H Harry J. Smith, <a href="/A063640/b063640.txt">Table of n, a(n) for n = 1..1000</a>
%p q:= n-> isprime(n) and numtheory[bigomega](n-1)=3:
%p select(q, [$2..1100])[]; # _Alois P. Heinz_, Mar 08 2023
%t Take[ Select[ Union@ Flatten@ Table[ Prime@p*Prime@q*Prime@r + 1, {p, 48}, {q, p}, {r, q}], PrimeQ@ # &], 53] (* Or *)
%t semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger[x] == 2; Select[Prime@ Range@ 182, semiPrimeQ[(# - 1)/2] &] (* _Robert G. Wilson v_, Sep 01 2007 *)
%t 2#+1&/@Select[Table[(n-1)/2,{n,Prime[Range[200]]}],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Oct 11 2018 *)
%o (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
%Y A090866 is a subsequence.
%Y Cf. A014612, A063639.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jul 21 2001