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

Author

Manuel Valdivia, Apr 09 2012

Keywords

• nonn
• more

Comments

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

Examples

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

Links

• Yves Gallot, Generalized Fermat Prime Search.
• OEIS Wiki, Generalized Fermat numbers.
• PrimeGrid, GFN Prime Search Status and History.

Crossrefs

Cf. A056993, A014574.

Programs

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.*)

Formula

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

Extensions

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