|
%I #29 Nov 17 2019 15:49:22
%S 3,3,3,75,113,2163,63739,13221,54809,3656571,6992033,125441,103859115,
%T 56414915,87888967
%N Adjacent generalized Fermat primes.
%C a(15)=87888967 but a(14) is unknown. - _Jeppe Stig Nielsen_, Mar 17 2018
%C The prime pair related to a(14) was found four days ago, and today double checking has proved that they are indeed the first occurrence for n=14. - _Jeppe Stig Nielsen_, May 02 2018
%H David Broadhurst, <a href="http://groups.yahoo.com/group/primeform/message/7397">Posting to PrimeForm</a> list.
%H David Broadhurst, Chris Caldwell and others, <a href="/A118539/a118539.txt">GFN near mid-air collision</a>, digest of 16 messages in primeform Yahoo group, May 2 - May 5, 2006. [Cached copy]
%H Yves Gallot's compilation of <a href="http://yves.gallot.pagesperso-orange.fr/primes/results.html">generalized Fermat</a> primes.
%F a(n) is the smallest number such that (a(n)+1)^(2^n)+1 and (a(n)-1)^(2^n)+1 are both prime.
%F a(n) = A217993(n) + 1. - _Jeppe Stig Nielsen_, Feb 27 2016
%e 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.
%Y Cf. A217993.
%K hard,more,nonn
%O 1,1
%A _David Broadhurst_, May 06 2006
%E a(13) from _Jeppe Stig Nielsen_, Mar 17 2018
%E a(14) and a(15) from _Jeppe Stig Nielsen_, May 02 2018
| 