A319217 Integers k such that (13*2^k)^8 + 1 is prime.

4, 9, 13, 38, 42, 67, 133, 134, 142, 155, 167, 226, 654, 5787, 6703, 12704, 25969, 70198, 78060, 235304

Offset

1,1

Comments

These numbers are a subset of Generalized Fermat Primes power 8.

All numbers from 1 to 235763 has been checked by LLR, no other primes found.

k is not congruent to 6 mod 25 because otherwise (13*2^k)^8+1 would be divisible by 401. - Bruno Berselli, Sep 21 2018

Links

Table of n, a(n) for n=1..20.

Chris K. Caldwell, The Prime Database: 815730721*2^1882432+1

Example

4 is a term because (13*2^4)^8+1 = 3503536769037500417 is a prime number.

Mathematica

Select[Range[700], PrimeQ[(13 2^#)^8 + 1] &] (* Vincenzo Librandi, Sep 21 2018 *)

Prog

(Magma) [n: n in [1..700] | IsPrime((13*2^n)^8+1)]; // Vincenzo Librandi, Sep 21 2018
(PARI) isok(k) = ispseudoprime((13*2^k)^8+1); \\ Altug Alkan, Sep 21 2018

Crossrefs

Sequence in context: A063606 A033287 A041323 * A041028 A041211 A042323

Adjacent sequences: A319214 A319215 A319216 * A319218 A319219 A319220

Keyword

nonn,hard,more

Author

Lei Zhou, Sep 13 2018

Status

approved