A235390 Numbers k such that k^(2^i)+1 are primes for i=0...5.

1, 7072833120, 9736020616, 12852419340, 36632235070, 41452651506, 44619665520, 53569833730, 54673378956, 66032908020, 69449109580, 69936419290, 82549220670, 99574135650, 106362659256, 108208833756, 113366066976, 136032409906, 167385272500, 174963279540, 195763339776

Offset

1,2

Comments

A subsequence of A070694.

Conjecture: the sequence is infinite.

For n=4 and n=9, a(n)*2+1 is also a prime.

The first term greater than 1 such that k^(2^6) + 1 is also prime, is a(148) = 2072005925466, see A335805. - Jeppe Stig Nielsen, Aug 18 2020

Links

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..101 (calculated by Yves Gallot (pers. communication), terms n = 2..94 from Martin Raab)

Yves Gallot, GFP (Generalized Fermat Progressions) / gfp6, software for calculating this sequence.

Example

k=7072833120 is in the sequence because the following are six primes: 7072833121, 7072833120^2+1, k^4+1, k^8+1, k^16+1, k^32+1.

Crossrefs

Cf. A000040, A006093, A019434, A056993, A070325, A070655, A070689, A070694, A090872, A335805.

Sequence in context: A199633 A288274 A078512 * A082255 A216867 A095926

Adjacent sequences: A235387 A235388 A235389 * A235391 A235392 A235393

Keyword

nonn

Author

Alex Ratushnyak, Jan 09 2014

Extensions

a(1)=1 inserted by Jeppe Stig Nielsen, Aug 11 2020

Status

approved