A182065 Smallest average of twin prime pairs s such that s^(2^n)+1 is prime.

4, 4, 4, 198, 30, 102, 3000, 7332, 4482, 187218, 150, 114690, 713310, 1943532, 3467622, 4470420, 23045178, 12529818

Offset

1,1

Comments

The averages of this sequence are base values in generalized Fermat primes.

Links

Table of n, a(n) for n=1..18.

Yves Gallot, Generalized Fermat Prime Search.

OEIS Wiki, Generalized Fermat numbers.

PrimeGrid, GFN Prime Search Status and History.

Formula

a(n) = (A014574(k))^(2^n)+1, for k = 1, 1, 1, 15, 5, 9, 82, 166, 117, 2055, 12, 1366, 6162, 14522, ...

Example

198^(2^4)+1 = 5580113648647376991977566450378407937 is prime.

Mathematica

t=Select[Table[Prime[n]+1, {n, 10^5}], PrimeQ[#1+1]&]; s:=t[[m]]; Table[m=1; While[!PrimeQ[s^(2^n)+1], m++]; s, {n, 1, 9}](* Last five terms obtained by intersection with Yves Gallot records.*)

Crossrefs

Cf. A056993, A014574.

Sequence in context: A217940 A353000 A372020 * A325487 A239351 A111481

Adjacent sequences: A182062 A182063 A182064 * A182066 A182067 A182068

Keyword

nonn,more

Author

Manuel Valdivia, Apr 09 2012

Extensions

a(15)-a(18) from Jeppe Stig Nielsen, Sep 14 2022

Status

approved