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 A118539 Adjacent generalized Fermat primes. 2
 3, 3, 3, 75, 113, 2163, 63739, 13221, 54809, 3656571, 6992033, 125441, 103859115, 56414915, 87888967 (list; graph; refs; listen; history; text; internal format)
 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 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. 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

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Last modified June 13 11:39 EDT 2021. Contains 344991 sequences. (Running on oeis4.)