A336115 Semiprimes that are product of a Fermat prime and a Mersenne prime.

9, 15, 21, 35, 51, 93, 119, 155, 381, 527, 635, 771, 1799, 2159, 7967, 24573, 32639, 40955, 139247, 196611, 393213, 458759, 655355, 1572861, 2031647, 2105087, 2228207, 2621435, 8323199, 8912879, 33685247, 134741759, 536813567, 6442450941, 8590000127, 10737418235

Offset: 1

Author

Antti Karttunen, Jul 09 2020

Keywords

• nonn

Comments

As 3 is both a Fermat prime and a Mersenne prime, A019434(1) * A000668(1) = 9 is also a term. It is the only square in this sequence.

Crossrefs

Cf. A000265, A000668, A019434, A144482, A333788, A335885.

Subsequence of A335912.

Programs

PARI

isA000668(n) = (isprime(n)&&!bitand(n,1+n));
isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2,n-1));
isA336115(n) = if(9==n,1, if((2!=omega(n))||(2!=bigomega(n)),0,my(ps=factor(n)[,1]); (isA019434(ps[1])&&isA000668(ps[2]))||(isA019434(ps[2])&&isA000668(ps[1])))); \\ Antti Karttunen, Jul 11 2020

Formula

A335885(a(n)) = 2.

Extensions

Missing terms and more terms added by Jinyuan Wang, Jul 11 2020