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%I #25 Sep 15 2022 06:27:19
%S 4,4,4,198,30,102,3000,7332,4482,187218,150,114690,713310,1943532,
%T 3467622,4470420,23045178,12529818
%N Smallest average of twin prime pairs s such that s^(2^n)+1 is prime.
%C The averages of this sequence are base values in generalized Fermat primes.
%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/GFN8192done.html">Generalized Fermat Prime Search</a>.
%H OEIS Wiki, <a href="/wiki/Generalized_Fermat_numbers">Generalized Fermat numbers</a>.
%H PrimeGrid, <a href="https://www.primegrid.com/gfn_history.php">GFN Prime Search Status and History</a>.
%F a(n) = (A014574(k))^(2^n)+1, for k = 1, 1, 1, 15, 5, 9, 82, 166, 117, 2055, 12, 1366, 6162, 14522, ...
%e 198^(2^4)+1 = 5580113648647376991977566450378407937 is prime.
%t t=Select[Table[Prime[n]+1,{n,10^5}],PrimeQ[#1+1]&]; s:=t[[m]]; Table[m=1; While[!PrimeQ[s^(2^n)+1],m++]; s,{n,1,9}](* Last five terms obtained by intersection with Yves Gallot records.*)
%Y Cf. A056993, A014574.
%K nonn,more
%O 1,1
%A _Manuel Valdivia_, Apr 09 2012
%E a(15)-a(18) from _Jeppe Stig Nielsen_, Sep 14 2022
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