A213246 Number of nonzero elements in GF(2^n) that are 9th powers.

1, 1, 7, 5, 31, 7, 127, 85, 511, 341, 2047, 455, 8191, 5461, 32767, 21845, 131071, 29127, 524287, 349525, 2097151, 1398101, 8388607, 1864135, 33554431, 22369621, 134217727, 89478485, 536870911, 119304647, 2147483647, 1431655765, 8589934591, 5726623061, 34359738367, 7635497415

Offset

1,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,65,0,0,0,0,0,-64).

Formula

a(n) = M / gcd( M, 9 ), where M=2^n-1.

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

a(n) = 65*a(n-6)-64*a(n-12).

G.f.: x*(2*x^2 -x +1)*(16*x^8 +16*x^7 +28*x^6 +16*x^5 +25*x^4 +8*x^3 +7*x^2 +2*x +1) / ((x -1)*(x +1)*(2*x -1)*(2*x +1)*(x^2 -x +1)*(x^2 +x +1)*(4*x^2 -2*x +1)*(4*x^2 +2*x +1)). (End)

Conjectures verified by Robert Israel, Jun 27 2018.

Maple

A213246:=n->(2^n-1)/gcd(2^n-1, 9): seq(A213246(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014

Mathematica

Table[(2^n - 1)/GCD[2^n - 1, 9], {n, 100}] (* Vincenzo Librandi, Mar 15 2013 *)

Prog

(Magma) [(2^n-1)/GCD(2^n-1, 9): n in [1..40]]; // Vincenzo Librandi, Mar 15 2013
(PARI) a(n)=(2^n-1)/gcd(2^n-1, 9) \\ Edward Jiang, Sep 04 2014
(GAP) List([1..40], n->(2^n-1)/Gcd(2^n-1, 9)); # Muniru A Asiru, Jun 27 2018

Crossrefs

Cf. A213243 (cubes), A213244 (5th powers), A213245 (7th powers), A213247 (11th powers), A213248 (13th powers).

Sequence in context: A334784 A146619 A059990 * A213243 A185269 A344917

Adjacent sequences: A213243 A213244 A213245 * A213247 A213248 A213249

Keyword

nonn,easy

Author

Joerg Arndt, Jun 07 2012

Status

approved