A213245 Number of nonzero elements in GF(2^n) that are 7th powers.

1, 3, 1, 15, 31, 9, 127, 255, 73, 1023, 2047, 585, 8191, 16383, 4681, 65535, 131071, 37449, 524287, 1048575, 299593, 4194303, 8388607, 2396745, 33554431, 67108863, 19173961, 268435455, 536870911, 153391689, 2147483647, 4294967295, 1227133513, 17179869183, 34359738367, 9817068105

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,9,0,0,-8).

Formula

a(n) = M / gcd( M, 7 ), where M=2^n-1.

Conjectures from Colin Barker, Aug 23 2014, verified by Robert Israel, Nov 20 2016: (Start)

a(n) = 9*a(n-3)-8*a(n-6).

G.f.: x*(4*x^4+6*x^3+x^2+3*x+1) / ( (x-1)*(2*x-1)*(x^2+x+1)*(4*x^2+2*x+1) ). (End)

Maple

A213245:=n->(2^n-1)/gcd(2^n-1, 7): seq(A213245(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014

Mathematica

Table[(2^n - 1)/GCD[2^n - 1, 7], {n, 60}] (* Vincenzo Librandi, Mar 16 2013 *)

Prog

(Magma) [(2^n - 1) / GCD (2^n - 1, 7): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013
(PARI) a(n)=(2^n-1)/gcd(2^n-1, 7) \\ Edward Jiang, Sep 04 2014

Crossrefs

Cf. A213243 (cubes), A213244 (5th powers), A213246 (9th powers), A213247 (11th powers), A213248 (13th powers).

Sequence in context: A284234 A365338 A089278 * A053485 A160628 A160604

Adjacent sequences: A213242 A213243 A213244 * A213246 A213247 A213248

Keyword

nonn,easy

Author

Joerg Arndt, Jun 07 2012

Status

approved