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