A253633 a(n) is the least positive integer b such that b^(2^n) + (b-1)^(2^n) is prime.

2, 2, 2, 2, 2, 9, 96, 32, 86, 60, 1079, 755, 312, 3509, 1829, 49958, 22845

Offset

0,1

Comments

When a(n) is 2, the corresponding prime is a Fermat prime, otherwise it is a so-called extended generalized Fermat prime sometimes denoted xGF(n, b, b-1) or similar.

Links

Table of n, a(n) for n=0..16.

Henri Lifchitz & Renaud Lifchitz, PRP Top Records, search for x^16384+y^16384, related to a(14).

Henri Lifchitz & Renaud Lifchitz, 49958^32768+49957^32768, a(15).

Henri Lifchitz & Renaud Lifchitz, 22845^65536+22844^65536, a(16).

Formula

a(n) = A080208(n) + 1.

Example

For n = 5, 2^5 = 32 is the exponent.  The numbers 1^32 + 0^32, 2^32 + 1^32, ..., 8^32 + 7^32 are not prime, but 9^32 + 8^32 is prime, so a(5) = 9. - Michael B. Porter, Mar 28 2018

Prog

(PARI) a(n)=for(b=2, 10^10, if(ispseudoprime(b^(2^n)+(b-1)^(2^n)), return(b)))

Crossrefs

Cf. A056993, A080208.

Sequence in context: A323443 A334511 A291944 * A216844 A088050 A260725

Adjacent sequences: A253630 A253631 A253632 * A253634 A253635 A253636

Keyword

nonn,hard,more

Author

Jeppe Stig Nielsen, Jan 07 2015

Extensions

a(13) from Jeppe Stig Nielsen, Mar 27 2018

a(14) found by Henri Lifchitz in 2007, from Jeppe Stig Nielsen, Apr 17 2018

a(15) found by Kellen Shenton, from Jeppe Stig Nielsen, Nov 27 2020

a(16) found by Kellen Shenton, from Jeppe Stig Nielsen, Mar 31 2021

Status

approved