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 *)
LinearRecurrence[{9, -30, 50, -45, 21, -4}, {1, 5, 32, 145, 512, 1649}, 30] (* Harvey P. Dale, Mar 06 2023 *)
PROG
(PARI) a(n)=1<<(n+n)+n^4
(Magma) [4^n+n^4: n in [0..30]]; // Vincenzo Librandi, Oct 27 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved