A334053 Least b such that b^(2^n) + 1 is a Proth prime (A080076).

2, 2, 2, 2, 2, 96, 6912, 960, 16256, 2013184, 235520, 61184, 125440, 992256, 155615232, 550207488, 12192710656

Offset: 0

Author

Jeppe Stig Nielsen, Sep 07 2020

Keywords

• more
• nonn

Comments

Every term b is in A116882 (the prime factor 2 of b must account for more than the square root of b).

For n up to about 11, a(n) can be found with the PARI function below. From there up to n=14, you can find a(n) by filtering lists of known primes of the form b^(2^n) + 1.

Links

• Chris K. Caldwell, The Prime Pages, 12192710656^65536 + 1

Crossrefs

Cf. A056993, A080076, A116882.

Programs

PARI

a(n) = forstep(b=2,+oo,2,2*valuation(b,2)>logint(b,2)&&ispseudoprime(b^(2^n)+1)&&return(b))

Extensions

a(15) calculated by Pavel Atnashev added by Jeppe Stig Nielsen, Sep 18 2020

a(16) calculated by Pavel Atnashev added by Jeppe Stig Nielsen, Jan 05 2021