A122528 - OEIS

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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, 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, n-1, 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 A359015

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