A000068 Numbers k such that k^4 + 1 is prime. (Formerly M1027 N0386)

1, 2, 4, 6, 16, 20, 24, 28, 34, 46, 48, 54, 56, 74, 80, 82, 88, 90, 106, 118, 132, 140, 142, 154, 160, 164, 174, 180, 194, 198, 204, 210, 220, 228, 238, 242, 248, 254, 266, 272, 276, 278, 288, 296, 312, 320, 328, 334, 340, 352, 364, 374, 414, 430, 436, 442, 466

Offset

1,2

References

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]

M. Lal, Primes of the form n^4 + 1, Math. Comp., 21 (1967), 245-247.

D. Shanks, On numbers of the form n^4+1, Math. Comp. 15 (74) (1961), 186-189.

Mathematica

Select[Range[10^2*2], PrimeQ[ #^4+1] &] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)

Prog

(PARI) {a(n) = local(m); if( n<1, 0, for(k=1, n, until( isprime(m^4 + 1), m++)); m)};
(PARI) list(lim)=my(v=List([1])); forstep(k=2, lim, 2, if(isprime(k^4+1), listput(v, k))); Vec(v) \\ Charles R Greathouse IV, Mar 31 2022
(Magma) [n: n in [0..800] | IsPrime(n^4+1)]; // Vincenzo Librandi, Nov 18 2010

Crossrefs

Cf. A002523, A037896, A005574, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A244150, A243959, A321323.

Sequence in context: A259939 A069654 A330359 * A067662 A248334 A001774

Adjacent sequences: A000065 A000066 A000067 * A000069 A000070 A000071

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved