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A122528 Minimal number k such that (2k)^(2^n) + 1 is prime, but (2k)^(2^m) + 1 is composite for m < n. 1

%I

%S 1,7,17,76,22,57,137,117,307,671,412,1279,767,35926,50915,35453,24297,

%T 114094,12259,37949,459722

%N Minimal number k such that (2k)^(2^n) + 1 is prime, but (2k)^(2^m) + 1 is composite for m < n.

%C A079706(a(n)) = 2^n which is the first occurrence of 2^n in A079706.

%C Corresponding primes A084712(a(n)) are {3, 197, 1336337, 284936905588473857, 197352587024076973231046657, ...}.

%H Yves Gallot et al., <a href="http://pagesperso-orange.fr/yves.gallot/primes/results.html">Generalized Fermat Prime Search</a>

%H PrimeGrid, <a href="http://www.primegrid.com/gfn_history.php">GFN Prime Search Status and History</a>.

%e a(0) = 1 because (2*1)^(2^0) + 1 = 2 + 1 = 3 is prime.

%e a(1) = 7 because (2*7)^(2^1) + 1 = 14^2 + 1 = 197 is prime but 14 + 1 = 15 is composite.

%o (PARI) a(n)=for(k=1,+oo,if(ispseudoprime((2*k)^(2^n)+1),for(m=0,n-1,ispseudoprime((2*k)^(2^m)+1)&&next(2));return(k))) \\ _Jeppe Stig Nielsen_, Mar 10 2018

%Y Cf. A079706, A084712.

%Y Cf. A056993.

%K hard,more,nonn

%O 0,2

%A _Alexander Adamchuk_, Sep 17 2006

%E Definition corrected by _T. D. Noe_, May 14 2008

%E a(9) through a(16) from the extensive tables of generalized Fermat primes compiled by Yves Gallot and others. - _T. D. Noe_, May 14 2008

%E a(17)-a(20) from _Jeppe Stig Nielsen_, Mar 10 2018

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Last modified June 18 06:02 EDT 2021. Contains 345098 sequences. (Running on oeis4.)