A213248 Number of nonzero elements in GF(2^n) that are 13th powers.

1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 315, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 1290555, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295, 8589934591, 17179869183, 34359738367, 5286113595

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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4097, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4096).

Formula

a(n) = M / gcd( M, 13 ) where M=2^n-1.

Conjectures from Colin Barker, Aug 24 2014: (Start)

a(n) = 4097*a(n-12)-4096*a(n-24).

G.f.: x*(2048*x^22 +3072*x^21 +3584*x^20 +3840*x^19 +3968*x^18 +4032*x^17 +4064*x^16 +4080*x^15 +4088*x^14 +4092*x^13 +4094*x^12 +315*x^11 +2047*x^10 +1023*x^9 +511*x^8 +255*x^7 +127*x^6 +63*x^5 +31*x^4 +15*x^3 +7*x^2 +3*x +1) / (4096*x^24 -4097*x^12 +1). (End)

Maple

A213248:=n->(2^n-1)/gcd(2^n-1, 13): seq(A213248(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014

Mathematica

Table[(2^n - 1)/GCD[2^n - 1, 13], {n, 40}] (* Vincenzo Librandi, Mar 17 2013 *)

Prog

(Magma) [(2^n - 1) / GCD (2^n - 1, 13): n in [1..40]]; // Vincenzo Librandi, Mar 17 2013
(PARI) a(n)=(2^n-1)/gcd(2^n-1, 13) \\ Edward Jiang, Sep 04 2014

Crossrefs

Cf. A213243 (cubes), A213244 (5th powers), A213245 (7th powers), A213246 (9th powers), A213247 (11th powers).

Sequence in context: A105755 A043764 A387418 * A336700 A387415 A097002

Adjacent sequences: A213245 A213246 A213247 * A213249 A213250 A213251

Keyword

nonn

Author

Joerg Arndt, Jun 07 2012

Status

approved