

A000059


Numbers n such that (2n)^4 + 1 is prime.
(Formerly M0867 N0332)


2



1, 2, 3, 8, 10, 12, 14, 17, 23, 24, 27, 28, 37, 40, 41, 44, 45, 53, 59, 66, 70, 71, 77, 80, 82, 87, 90, 97, 99, 102, 105, 110, 114, 119, 121, 124, 127, 133, 136, 138, 139, 144, 148, 156, 160, 164, 167, 170, 176, 182, 187, 207, 215, 218, 221, 233, 236, 238, 244, 246
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OFFSET

1,2


REFERENCES

J. Bohman, New primes of the form n^4+1, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 370372.
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
M. Lal, Primes of the form n^4 + 1, Math. Comp., 21 (1967), 245247.


FORMULA

a(n) = A000068(n)/2 for n > 1.


EXAMPLE

(2 * 2)^4 + 1 = 4^4 + 1 = 17, which is prime, so 2 is in the sequence.
(2 * 3)^4 + 1 = 6^4 + 1 = 1297, which is prime, so 3 is in the sequence.
(2 * 4)^4 + 1 = 8^4 + 1 = 4097 = 17 * 241, so 4 is not in the sequence.


MAPLE

A000059:=n>`if`(isprime((2*n)^4+1), n, NULL): seq(A000059(n), n=1..250); # Wesley Ivan Hurt, Aug 26 2014


MATHEMATICA

Select[Range[300], PrimeQ[(2 * #)^4 + 1] &] (* Vladimir Joseph Stephan Orlovsky, Jan 24 2012 *)


PROG

(PARI) for(n=1, 10^3, if(isprime( (2*n)^4+1 ), print1(n, ", "))) \\ Hauke Worpel (thebigh(AT)outgun.com), Jun 11 2008 [edited by Michel Marcus, Aug 27 2014]
(MAGMA)[n: n in [1..10000]  IsPrime((2*n)^4+1)] # Vincenzo Librandi, Nov 18 2010
(Python)
from sympy import isprime
for n in range(10**3):
..if isprime(16*n**4+1):
....print(n, end=', ')
# Derek Orr, Aug 27 2014


CROSSREFS

Cf. A037896 primes of the form n^4 + 1.
Sequence in context: A028751 A057543 A190650 * A216761 A276559 A097053
Adjacent sequences: A000056 A000057 A000058 * A000060 A000061 A000062


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Hugo Pfoertner, Aug 27 2003


STATUS

approved



