A386295 Primes p such that p+1 is a triprime and 2*p+1 is prime.

11, 29, 41, 113, 173, 281, 641, 653, 761, 1901, 2273, 2693, 2741, 3413, 3593, 5441, 6053, 6113, 6521, 6581, 7121, 7841, 9293, 9473, 10253, 10733, 12101, 12821, 14081, 14621, 15233, 16493, 19301, 19373, 19553, 19913, 20441, 20693, 21341, 21701, 22433, 24473, 27281, 27581, 27893, 28793, 28901

Offset: 1

Author

Zak Seidov and Robert Israel, Jul 17 2025

Keywords

• nonn

Comments

Sophie Germain primes of the form p*q*r - 1, where p, q and r are primes.

Except for 11, all terms == 5 (mod 12).

Examples

			a(3) = 41 is a term because it is prime, 41 + 1 = 42 = 2 * 3 * 7 is a triprime, and 41 * 2 + 1 = 83 is prime.
		

Links

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

Crossrefs

Cf. A014612.

Intersection of A005384 and A063639.

Programs

Maple

select(p -> isprime(p) and isprime(2*p+1) and numtheory:-bigomega(p+1) = 3, [seq(i,i=3..30000,2)]);

Mathematica

s= {}; Do[p = Prime[k]; If[3 == PrimeOmega[p + 1] && PrimeQ[2*p +1], AppendTo[s, p]], {k, 2000}];s