

A118539


Adjacent generalized Fermat primes.


2



3, 3, 3, 75, 113, 2163, 63739, 13221, 54809, 3656571, 6992033, 125441, 103859115, 56414915, 87888967
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OFFSET

1,1


COMMENTS

a(15)=87888967 but a(14) is unknown.  Jeppe Stig Nielsen, Mar 17 2018
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


LINKS

Table of n, a(n) for n=1..15.
David Broadhurst, Posting to PrimeForm list.
David Broadhurst, Chris Caldwell and others, GFN near midair collision, digest of 16 messages in primeform Yahoo group, May 2  May 5, 2006. [Cached copy]
Yves Gallot's compilation of generalized Fermat primes.


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


EXAMPLE

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.


CROSSREFS

Cf. A217993.
Sequence in context: A091323 A174641 A217671 * A015665 A343120 A230667
Adjacent sequences: A118536 A118537 A118538 * A118540 A118541 A118542


KEYWORD

hard,more,nonn


AUTHOR

David Broadhurst, May 06 2006


EXTENSIONS

a(13) from Jeppe Stig Nielsen, Mar 17 2018
a(14) and a(15) from Jeppe Stig Nielsen, May 02 2018


STATUS

approved



