login
A319217
Integers k such that (13*2^k)^8 + 1 is prime.
1
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
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
KEYWORD
nonn,hard,more
AUTHOR
Lei Zhou, Sep 13 2018
STATUS
approved