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A118539
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Adjacent generalized Fermat primes.
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2
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3, 3, 3, 75, 113, 2163, 63739, 13221, 54809, 3656571, 6992033, 125441, 103859115, 56414915, 87888967
(list;
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listen;
history;
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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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]
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FORMULA
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a(n) is the smallest number such that (a(n)+1)^(2^n)+1 and (a(n)-1)^(2^n)+1 are both prime.
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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