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A213244 Number of nonzero elements in GF(2^n) that are 5th powers. 7
1, 3, 7, 3, 31, 63, 127, 51, 511, 1023, 2047, 819, 8191, 16383, 32767, 13107, 131071, 262143, 524287, 209715, 2097151, 4194303, 8388607, 3355443, 33554431, 67108863, 134217727 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

a(n) = M / GCD( M, 5 ) where M=2^n-1.

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

a(n) = 17*a(n-4)-16*a(n-8).

G.f.: x*(8*x^6+12*x^5+14*x^4+3*x^3+7*x^2+3*x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)*(x^2+1)*(4*x^2+1)).

(End)

MAPLE

A213244:=n->(2^n-1)/gcd(2^n-1, 5): seq(A213244(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014

MATHEMATICA

Table[(2^n - 1)/GCD[2^n - 1, 5], {n, 50}] (* Vincenzo Librandi, Mar 16 2013 *)

PROG

(MAGMA) [(2^n - 1) / GCD (2^n - 1, 5): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013

(PARI) a(n)=(2^n-1)/gcd(2^n-1, 5) \\ Edward Jiang, Sep 04 2014

CROSSREFS

Cf. A213243 (cubes), A213245 (7th powers), A213246 (9th powers), A213247 (11th powers), A213248 (13th powers).

Sequence in context: A086153 A049479 A125314 * A050393 A110778 A200129

Adjacent sequences:  A213241 A213242 A213243 * A213245 A213246 A213247

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jun 07 2012

STATUS

approved

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Last modified November 18 18:46 EST 2017. Contains 294894 sequences.