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A006313 Numbers n such that n^16 + 1 is prime.
(Formerly M2164)
43

%I M2164 #51 Sep 08 2022 08:44:34

%S 1,2,44,74,76,94,156,158,176,188,198,248,288,306,318,330,348,370,382,

%T 396,452,456,470,474,476,478,560,568,598,642,686,688,690,736,774,776,

%U 778,790,830,832,834,846,900,916,946,956,972,982,984,1018,1044,1078

%N Numbers n such that n^16 + 1 is prime.

%D Dubner, Harvey. "Generalized Fermat primes." J. Recreational Math., 18 (1985): 279-280.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Ray Chandler, <a href="/A006313/b006313.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%t lst={};Do[If[PrimeQ[n^16+1], AppendTo[lst, n]], {n, 10^4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 20 2008 *)

%t s=Reap[Sow[1];Do[If[PrimeQ[n^16+1],Sow[n]],{n,2,40352,2}]][[2,1]] (* _Zak Seidov_, Dec 22 2010 *)

%t Join[{1},2*Flatten[Position[Range[2,1100,2]^16+1,_?PrimeQ]]] (* _Harvey P. Dale_, Jun 26 2017 *)

%o (PARI) isA006313(n) = isprime(n^16+1) \\ _Michael B. Porter_, Mar 25 2010

%o (Magma) [ n: n in [0..1500] | IsPrime(n^16+1) ]; // _Vincenzo Librandi_, Nov 18 2010

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

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Hugo Pfoertner_, Jun 22 2003

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)