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

1,1

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.

Links

Table of n, a(n) for n=1..36.

Formula

A335885(a(n)) = 2.

Prog

(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

Crossrefs

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

Subsequence of A335912.

Sequence in context: A241809 A063174 A338082 * A072569 A072572 A029708

Adjacent sequences: A336112 A336113 A336114 * A336116 A336117 A336118

Keyword

nonn

Author

Antti Karttunen, Jul 09 2020

Extensions

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

Status

approved