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

1,1

Comments

All terms == 1 (mod 12).

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

Links

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

Example

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.

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)]);

Prog

(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

Crossrefs

Contained in A005383, A100363 and A112998.

Sequence in context: A065213 A100363 A142500 * A347636 A113000 A105129

Adjacent sequences: A328134 A328135 A328136 * A328138 A328139 A328140

Keyword

nonn

Author

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

Status

approved