A001593 a(n) = 5^n + n^5.

1, 6, 57, 368, 1649, 6250, 23401, 94932, 423393, 2012174, 9865625, 48989176, 244389457, 1221074418, 6104053449, 30518337500, 152588939201, 762940872982, 3814699155193, 19073488804224, 95367434840625, 476837162287226, 2384185796169257, 11920928961514468

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(24) is prime; a(1036) and a(104824) are probable primes (3-PRP). - David Radcliffe, Dec 23 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-45,95,-115,81,-31,5).

Crossrefs

Cf. A001580, A001585, A001589.

Programs

Magma

[5^n+n^5: n in [0..30]]; // Vincenzo Librandi, Oct 27 2011

Maple

seq(seq(k^n+n^k, k=5..5), n=0..20); # Zerinvary Lajos, Jun 29 2007

Mathematica

f[n_]:=5^n+n^5;f[Range[0,40]] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2011 *)
LinearRecurrence[{11,-45,95,-115,81,-31,5},{1,6,57,368,1649,6250,23401},30] (* Harvey P. Dale, Jan 15 2018 *)

PARI

a(n)=5^n+n^5 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (4*x^6+135*x^5+289*x^4+84*x^3-36*x^2+5*x-1) / ((x-1)^6*(5*x-1)). - Colin Barker, May 07 2013

Extensions

More terms from Colin Barker, May 07 2013