A006313 Numbers k such that k^16 + 1 is prime.

1, 2, 44, 74, 76, 94, 156, 158, 176, 188, 198, 248, 288, 306, 318, 330, 348, 370, 382, 396, 452, 456, 470, 474, 476, 478, 560, 568, 598, 642, 686, 688, 690, 736, 774, 776, 778, 790, 830, 832, 834, 846, 900, 916, 946, 956, 972, 982, 984, 1018, 1044, 1078

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• Dubner, Harvey. "Generalized Fermat primes." J. Recreational Math., 18 (1985): 279-280.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A005574, A000068, A006314, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A244150, A243959, A321323.

Programs

Magma

[ n: n in [0..1500] | IsPrime(n^16+1) ]; // Vincenzo Librandi, Nov 18 2010

Mathematica

lst={};Do[If[PrimeQ[n^16+1], AppendTo[lst, n]], {n, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 20 2008 *)
s=Reap[Sow[1];Do[If[PrimeQ[n^16+1],Sow[n]],{n,2,40352,2}]][[2,1]] (* Zak Seidov, Dec 22 2010 *)
Join[{1},2*Flatten[Position[Range[2,1100,2]^16+1,?PrimeQ]]] (* _Harvey P. Dale, Jun 26 2017 *)

PARI

isA006313(n) = isprime(n^16+1) \\ Michael B. Porter, Mar 25 2010

Extensions

More terms from Hugo Pfoertner, Jun 22 2003