

A122528


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


1



1, 7, 17, 76, 22, 57, 137, 117, 307, 671, 412, 1279, 767, 35926, 50915, 35453, 24297, 114094, 12259, 37949, 459722
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OFFSET

0,2


COMMENTS

A079706(a(n)) = 2^n which is the first occurrence of 2^n in A079706.
Corresponding primes A084712(a(n)) are {3, 197, 1336337, 284936905588473857, 197352587024076973231046657, ...}.


LINKS

Table of n, a(n) for n=0..20.
Yves Gallot et al., Generalized Fermat Prime Search
PrimeGrid, GFN Prime Search Status and History.


EXAMPLE

a(0) = 1 because (2*1)^(2^0) + 1 = 2 + 1 = 3 is prime.
a(1) = 7 because (2*7)^(2^1) + 1 = 14^2 + 1 = 197 is prime but 14 + 1 = 15 is composite.


PROG

(PARI) a(n)=for(k=1, +oo, if(ispseudoprime((2*k)^(2^n)+1), for(m=0, n1, ispseudoprime((2*k)^(2^m)+1)&&next(2)); return(k))) \\ Jeppe Stig Nielsen, Mar 10 2018


CROSSREFS

Cf. A079706, A084712.
Cf. A056993.
Sequence in context: A086870 A107693 A217717 * A123206 A035078 A177123
Adjacent sequences: A122525 A122526 A122527 * A122529 A122530 A122531


KEYWORD

hard,more,nonn


AUTHOR

Alexander Adamchuk, Sep 17 2006


EXTENSIONS

Definition corrected by T. D. Noe, May 14 2008
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
a(17)a(20) from Jeppe Stig Nielsen, Mar 10 2018


STATUS

approved



