A213247 Number of nonzero elements in GF(2^n) that are 11th powers.

1, 3, 7, 15, 31, 63, 127, 255, 511, 93, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 95325, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 97612893, 2147483647, 4294967295, 8589934591, 17179869183, 34359738367, 68719476735

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, 1025, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1024).

Formula

a(n) = M / GCD( M, 11 ) where M=2^n-1.

From Colin Barker, Aug 24 2014: (Start)

a(n) = 1025*a(n-10)-1024*a(n-20).

G.f.: x*(512*x^18 +768*x^17 +896*x^16 +960*x^15 +992*x^14 +1008*x^13 +1016*x^12 +1020*x^11 +1022*x^10 +93*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) / (1024*x^20 -1025*x^10 +1).

(End)

a(n) = (2^n - 1)/11 if n is divisible by 10, 2^n - 1 otherwise. - Robert Israel, Aug 24 2014

Maple

A213247:=n->(2^n-1)/igcd(2^n-1, 11): seq(A213247(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014

Mathematica

Table[(2^n - 1)/GCD[2^n - 1, 11], {n, 50}] (* Vincenzo Librandi, Mar 16 2013 *)

Prog

(Magma) [(2^n - 1) / GCD (2^n - 1, 11): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013
(PARI) { for(n=1, 36, if(n%10, a=2^n-1, a=(2^n-1)/11); print1(a, ", ")) } \\ K. Spage, Aug 23 2014

Crossrefs

Cf. A213243 (cubes), A213244 (5th powers), A213245 (7th powers), A213246 (9th powers), A213248 (13th powers).

Sequence in context: A116690 A267258 A305493 * A043755 A105755 A043764

Adjacent sequences: A213244 A213245 A213246 * A213248 A213249 A213250

Keyword

nonn

Author

Joerg Arndt, Jun 07 2012

Status

approved