A328137 Primes p such that p+1 is the product of two distinct primes and p+2 is the product of three distinct primes.

193, 397, 613, 661, 757, 1093, 1237, 1453, 1657, 2137, 2341, 2593, 2917, 3217, 4177, 4621, 5233, 6121, 6133, 7057, 7537, 8101, 8317, 8353, 8677, 8893, 9013, 9721, 10957, 11677, 11701, 12421, 12433, 12541, 12853, 13933, 15277, 15733, 16033, 16381, 16417, 16633, 17257, 17293, 18013, 18253, 18481

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 04 2019

Keywords

• nonn

Comments

All terms == 1 (mod 12).

Members k of A112998 such that k+2 is squarefree.

Examples

			a(3)=613 is in the sequence because 613 is prime, 614=2*307 is the product of two distinct primes, and 615=3*5*41 is the product of three distinct primes.
		

Links

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

Crossrefs

Contained in A005383, A100363 and A112998.

Programs

Magma

[p:p in PrimesUpTo(20000)| IsPrime((p+1) div 2) and IsSquarefree(p+2) and #PrimeDivisors(p+2) eq 3]; // Marius A. Burtea, Oct 04 2019

Maple

select(t -> isprime(t) and isprime((t+1)/2) and numtheory:-issqrfree(t+2) and numtheory:-bigomega(t+2)=3, [seq(i,i=1..10^5,12)]);