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A253633 a(n) is the least positive integer b such that b^(2^n) + (b-1)^(2^n) is prime.

%I A253633 #31 Jun 07 2021 01:15:05
%S A253633 2,2,2,2,2,9,96,32,86,60,1079,755,312,3509,1829,49958,22845
%N A253633 a(n) is the least positive integer b such that b^(2^n) + (b-1)^(2^n) is prime.
%C A253633 When a(n) is 2, the corresponding prime is a Fermat prime, otherwise it is a so-called extended generalized Fermat prime sometimes denoted xGF(n, b, b-1) or similar.
%H A253633 Henri Lifchitz & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=x%5E16384%2By%5E16384">PRP Top Records, search for x^16384+y^16384</a>, related to a(14).
%H A253633 Henri Lifchitz & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=49958%5E32768%2B49957%5E32768">49958^32768+49957^32768</a>, a(15).
%H A253633 Henri Lifchitz & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=22845%5E65536%2B22844%5E65536">22845^65536+22844^65536</a>, a(16).
%F A253633 a(n) = A080208(n) + 1.
%e A253633 For n = 5, 2^5 = 32 is the exponent.  The numbers 1^32 + 0^32, 2^32 + 1^32, ..., 8^32 + 7^32 are not prime, but 9^32 + 8^32 is prime, so a(5) = 9. - _Michael B. Porter_, Mar 28 2018
%o A253633 (PARI) a(n)=for(b=2,10^10,if(ispseudoprime(b^(2^n)+(b-1)^(2^n)),return(b)))
%Y A253633 Cf. A056993, A080208.
%K A253633 nonn,hard,more
%O A253633 0,1
%A A253633 _Jeppe Stig Nielsen_, Jan 07 2015
%E A253633 a(13) from _Jeppe Stig Nielsen_, Mar 27 2018
%E A253633 a(14) found by _Henri Lifchitz_ in 2007, from _Jeppe Stig Nielsen_, Apr 17 2018
%E A253633 a(15) found by _Kellen Shenton_, from _Jeppe Stig Nielsen_, Nov 27 2020
%E A253633 a(16) found by _Kellen Shenton_, from _Jeppe Stig Nielsen_, Mar 31 2021