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

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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)

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 *)

Prog

(Magma) [(2^n - 1) / GCD (2^n - 1, 5): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013
(PARI) a(n)=(2^n-1)/gcd(2^n-1, 5) \\ Edward Jiang, Sep 04 2014

Crossrefs

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

Sequence in context: A366141 A049479 A125314 * A050393 A110778 A200129

Adjacent sequences: A213241 A213242 A213243 * A213245 A213246 A213247

Keyword

nonn

Author

Joerg Arndt, Jun 07 2012

Status

approved