

A328137


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


2



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
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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



