A303448 Numbers m such that both m and (m-1)/2 are Fermat pseudoprimes base 2 (A001567).

19781763, 46912496118443, 192153584101141163

Offset: 1

Author

Max Alekseyev, Apr 24 2018

Keywords

• bref
• hard
• more
• nonn

Comments

No other terms below 2^65.

Terms a(2) and a(3) are of the form (2^(2k+1)+1)/3 = A007583(k).

Terms A007583(k) belong to this sequence for k in A303009. Correspondingly, a(4) <= A007583(A303009(3)) = (2^83+1)/3 = 3223802185639011132549803.

If a(n) is not divisible by 3, then it also belongs to A175625.

Crossrefs

Numbers (a(n)-1)/2 are listed in A303447.

Subsequence of A006970 and A300193.

Cf. A175625, A175942, A298758.

Formula

a(n) = 2*A303447(n) + 1.

Extensions

a(1) from Amiram Eldar, Jan 26 2018