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A253633 a(n) is least natural number b such that b^(2^n) + (b-1)^(2^n) is prime. 4

%I

%S 2,2,2,2,2,9,96,32,86,60,1079,755,312,3509,1829,49958

%N a(n) is least natural number b such that b^(2^n) + (b-1)^(2^n) is prime.

%C 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 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).

%F a(n) = A080208(n) + 1.

%e 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 (PARI) a(n)=for(b=2,10^10,if(ispseudoprime(b^(2^n)+(b-1)^(2^n)),return(b)))

%Y Cf. A056993, A080208.

%K nonn,hard,more

%O 0,1

%A _Jeppe Stig Nielsen_, Jan 07 2015

%E a(13) from _Jeppe Stig Nielsen_, Mar 27 2018

%E a(14) found by Henri Lifchitz in 2007, from _Jeppe Stig Nielsen_, Apr 17 2018

%E a(15) found by _Kellen Shenton_, from _Jeppe Stig Nielsen_, Nov 27 2020

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Last modified March 2 09:23 EST 2021. Contains 341746 sequences. (Running on oeis4.)