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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

N. J. A. Sloane

STATUS

approved

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Last modified September 20 10:10 EDT 2019. Contains 327229 sequences. (Running on oeis4.)