OFFSET
1,2
REFERENCES
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
J. Bohman, New primes of the form n^4+1, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 370-372.
M. Lal, Primes of the form n^4 + 1, Math. Comp., 21 (1967), 245-247.
FORMULA
a(n) = A000068(n+1)/2 for n >= 1. [Corrected by Jianing Song, Feb 03 2019]
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
print([n for n in range(10**3) if isprime(16*n**4+1)])
# Derek Orr, Aug 27 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Hugo Pfoertner, Aug 27 2003
STATUS
approved