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%I #23 May 20 2023 15:10:51
%S 1,1,1,1,1,8,95,31,85,59,1078,754,311,3508,1828,49957,22844
%N a(n) is the least k such that the generalized Fermat number (k+1)^(2^n) + k^(2^n) is prime.
%C The first five terms correspond to the five known Fermat primes. The sequence A078902 lists some of the generalized Fermat primes. Bjorn and Riesel examined generalized Fermat numbers for k <= 11 and n <= 999. The sequence A080134 lists the conjectured number of primes for each k.
%C For n >= 10, a(n) yields a probable prime. a(13) was found by _Henri Lifchitz_. It is known that a(14) > 1000.
%H T. D. Noe, <a href="http://www.sspectra.com/math/GenFermatPrimes.txt">Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m</a>
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-98-00891-6">Factors of generalized Fermat numbers</a>, Math. Comp. 67 (1998), no. 221, pp. 441-446.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>
%F a(n) = A253633(n) - 1.
%e a(5) = 8 because (k+1)^32 + k^32 is prime for k = 8 and composite for k < 8.
%Y Cf. A019434, A078902, A080134, A153504, A152913, A194185, A253633.
%K hard,more,nonn
%O 0,6
%A _T. D. Noe_, Feb 10 2003
%E a(14)-a(15) from _Jeppe Stig Nielsen_, Nov 27 2020
%E a(16) by _Kellen Shenton_ communicated by _Jeppe Stig Nielsen_, May 19 2023
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