A350409 Primes p such that 2*p+1 has exactly three prime factors (not necessarily distinct).

13, 31, 37, 73, 97, 103, 127, 137, 139, 181, 193, 199, 211, 227, 241, 269, 277, 307, 313, 331, 373, 379, 397, 433, 457, 463, 467, 541, 547, 563, 571, 587, 617, 619, 647, 709, 727, 733, 739, 751, 757, 773, 797, 829, 859, 883, 887, 929, 977, 1021, 1033, 1069, 1117, 1123

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For p = 31, 2*p+1 = 63, which factors as 3*3*7.
For p = 97, 2*p+1 = 195, which factors as 3*5*13.

Maple

filter:= proc(p) isprime(p) and numtheory:-bigomega(2*p+1)=3 end proc:
select(filter, [seq(i, i=3..2000, 2)]); # Robert Israel, Nov 09 2022

Mathematica

Select[Prime@Range@200, PrimeOmega[2#+1]==3&] (* Giorgos Kalogeropoulos, Jan 08 2022 *)

Prog

(PARI) is(n) = bigomega(2*n + 1) == 3 && isprime(n) \\ David A. Corneth, Jan 06 2022

Crossrefs

Sequence in context: A023274 A349636 A129864 * A080387 A348300 A100589

Adjacent sequences: A350406 A350407 A350408 * A350410 A350411 A350412

Keyword

nonn,easy

Author

Paul Duckett, Jan 06 2022

Extensions

More terms from David A. Corneth, Jan 06 2022

Status

approved