A213244 Number of nonzero elements in GF(2^n) that are 5th powers.

1, 3, 7, 3, 31, 63, 127, 51, 511, 1023, 2047, 819, 8191, 16383, 32767, 13107, 131071, 262143, 524287, 209715, 2097151, 4194303, 8388607, 3355443, 33554431, 67108863, 134217727

Offset: 1

Author

Joerg Arndt, Jun 07 2012

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 17, 0, 0, 0, -16).

Crossrefs

Cf. A213243 (cubes), A213245 (7th powers), A213246 (9th powers), A213247 (11th powers), A213248 (13th powers).

Programs

Magma

[(2^n - 1) / GCD (2^n - 1, 5): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013

Maple

A213244:=n->(2^n-1)/gcd(2^n-1,5): seq(A213244(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014

Mathematica

Table[(2^n - 1)/GCD[2^n - 1, 5], {n, 50}] (* Vincenzo Librandi, Mar 16 2013 *)

PARI

a(n)=(2^n-1)/gcd(2^n-1,5) \\ Edward Jiang, Sep 04 2014

Formula

a(n) = M / GCD( M, 5 ) where M=2^n-1.

Conjectures from Colin Barker, Aug 23 2014: (Start)

a(n) = 17*a(n-4)-16*a(n-8).

G.f.: x*(8*x^6+12*x^5+14*x^4+3*x^3+7*x^2+3*x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)*(x^2+1)*(4*x^2+1)).

(End)