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

Offset: 0

Author

Alexander Adamchuk, Sep 17 2006

Keywords

• hard
• more
• nonn

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, ...}.

Examples

			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.
		

Links

• Yves Gallot et al., Generalized Fermat Prime Search
• PrimeGrid, GFN Prime Search Status and History.

Crossrefs

Cf. A079706, A084712.

Cf. A056993.

Programs

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

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