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

%I #22 Jan 05 2021 03:44:44

%S 2,2,2,2,2,96,6912,960,16256,2013184,235520,61184,125440,992256,

%T 155615232,550207488,12192710656

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

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

%C 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.

%H Chris K. Caldwell, The Prime Pages, <a href="https://primes.utm.edu/primes/page.php?id=131541">12192710656^65536 + 1</a>

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

%Y Cf. A056993, A080076, A116882.

%K more,nonn

%O 0,1

%A _Jeppe Stig Nielsen_, Sep 07 2020

%E a(15) calculated by Pavel Atnashev added by _Jeppe Stig Nielsen_, Sep 18 2020

%E a(16) calculated by Pavel Atnashev added by _Jeppe Stig Nielsen_, Jan 05 2021