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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES J. Bohman, New primes of the form n^4+1, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 370-372. 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), 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, 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: A325424 A057543 A190650 * A216761 A276559 A097053 Adjacent sequences:  A000056 A000057 A000058 * A000060 A000061 A000062 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Hugo Pfoertner, Aug 27 2003 STATUS approved

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Last modified October 21 04:26 EDT 2019. Contains 328291 sequences. (Running on oeis4.)