A118539 Adjacent generalized Fermat primes.
3, 3, 3, 75, 113, 2163, 63739, 13221, 54809, 3656571, 6992033, 125441, 103859115, 56414915, 87888967
Offset: 1
Examples
a(11)=6992033 because 6992034^2048+1 is prime, 6992032^2048+1 is prime and no smaller pair of bases differing by 2 gives a pair of primes with the exponent 2^11=2048.
Links
- David Broadhurst, Posting to PrimeForm list.
- David Broadhurst, Chris Caldwell and others, GFN near mid-air collision, digest of 16 messages in primeform Yahoo group, May 2 - May 5, 2006. [Cached copy]
- Yves Gallot's compilation of generalized Fermat primes.
Crossrefs
Cf. A217993.
Formula
a(n) is the smallest number such that (a(n)+1)^(2^n)+1 and (a(n)-1)^(2^n)+1 are both prime.
a(n) = A217993(n) + 1. - Jeppe Stig Nielsen, Feb 27 2016
Extensions
a(13) from Jeppe Stig Nielsen, Mar 17 2018
a(14) and a(15) from Jeppe Stig Nielsen, May 02 2018
Comments