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%I #17 Nov 27 2022 11:06:17
%S 2,2,2,4,2,49592,7132,532,333482,2226686,3543554,23379038,1249625230,
%T 188489906
%N Smallest k >= 2 such that k^(2^n)+1 is the lesser member of a twin prime pair.
%C These lesser of twin prime pairs are also generalized Fermat primes, (not possible for greater of twin prime pairs, except for 5).
%C When extending this sequence, it is useful if the primes b^(2^n)+1 are known in advance (Gallot link). - _Jeppe Stig Nielsen_, Sep 25 2019
%C For later terms, the bigger twin is only a probable prime, not a proven prime. - _Jeppe Stig Nielsen_, Nov 24 2022
%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/results.html">Generalized Fermat Prime Search</a>.
%H OEIS Wiki, <a href="/wiki/Generalized_Fermat_numbers">Generalized Fermat numbers</a>.
%H PrimeGrid and "Stream", <a href="https://www.primegrid.com/forum_thread.php?id=9538">GFN-1x Small Primes search</a>, mentions a(12) and a(13).
%e 2^(2^4)+1 = 65537 = A001359(861), then a(4) = 2.
%t Table[k=2; While[!PrimeQ[k^(2^n)+1]||!PrimeQ[k^(2^n +3],k++]; k,{n,0,7}]
%Y Cf. A056993, A001359.
%K nonn,more,hard
%O 0,1
%A _Manuel Valdivia_, Apr 15 2012
%E a(8)-a(10) from _Jeppe Stig Nielsen_, Sep 25 2019
%E Name edited by _Felix Fröhlich_, Sep 25 2019
%E a(11)-a(13) from _Jeppe Stig Nielsen_, Nov 24 2022
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