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 A001589 a(n) = 4^n + n^4. 11
 1, 5, 32, 145, 512, 1649, 5392, 18785, 69632, 268705, 1058576, 4208945, 16797952, 67137425, 268473872, 1073792449, 4295032832, 17179952705, 68719581712, 274878037265, 1099511787776, 4398046705585, 17592186278672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is prime if and only if n = 1. - Reinhard Zumkeller, May 24 2009 The statement above (and the corollary that 5 is the only prime term in this sequence) can be proved using Sophie Germain's identity x^4 + 4y^4 = (x^2 + 2xy + 2y^2)(x^2 - 2xy + 2y^2). - Alonso del Arte, Oct 31 2013 [exponents corrected by Thomas Ordowski, Nov 29 2017] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Notes, Mathematical Intelligencer 2(2) (1980), p. 66. - Reinhard Zumkeller, May 24 2009 Index entries for linear recurrences with constant coefficients, signature (9,-30,50,-45,21,-4). FORMULA G.f.: -(5*x^5 + 38*x^4 + 43*x^3 - 17*x^2 + 4*x - 1) / ((x - 1)^5*(4*x - 1)). - Colin Barker, Jan 01 2013 MATHEMATICA Table[4^n + n^4, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2011 *) PROG (PARI) a(n)=1<<(n+n)+n^4 (MAGMA) [4^n+n^4: n in [0..30]]; // Vincenzo Librandi, Oct 27 2011 CROSSREFS Cf. A001580, A001585. Sequence in context: A077207 A319790 A273623 * A271903 A177467 A268153 Adjacent sequences:  A001586 A001587 A001588 * A001590 A001591 A001592 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)