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A213245 Number of nonzero elements in GF(2^n) that are 7th powers. 8
1, 3, 1, 15, 31, 9, 127, 255, 73, 1023, 2047, 585, 8191, 16383, 4681, 65535, 131071, 37449, 524287, 1048575, 299593, 4194303, 8388607, 2396745, 33554431, 67108863, 19173961, 268435455, 536870911, 153391689, 2147483647, 4294967295, 1227133513, 17179869183, 34359738367, 9817068105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,9,0,0,-8).

FORMULA

a(n) = M / gcd( M, 7 ), where M=2^n-1.

Conjectures from Colin Barker, Aug 23 2014, verified by Robert Israel, Nov 20 2016: (Start)

a(n) = 9*a(n-3)-8*a(n-6).

G.f.: x*(4*x^4+6*x^3+x^2+3*x+1) / ( (x-1)*(2*x-1)*(x^2+x+1)*(4*x^2+2*x+1) ). (End)

MAPLE

A213245:=n->(2^n-1)/gcd(2^n-1, 7): seq(A213245(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014

MATHEMATICA

Table[(2^n - 1)/GCD[2^n - 1, 7], {n, 60}] (* Vincenzo Librandi, Mar 16 2013 *)

PROG

(MAGMA) [(2^n - 1) / GCD (2^n - 1, 7): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013

(PARI) a(n)=(2^n-1)/gcd(2^n-1, 7) \\ Edward Jiang, Sep 04 2014

CROSSREFS

Cf. A213243 (cubes), A213244 (5th powers), A213246 (9th powers), A213247 (11th powers), A213248 (13th powers).

Sequence in context: A284861 A284234 A089278 * A087071 A053485 A160628

Adjacent sequences:  A213242 A213243 A213244 * A213246 A213247 A213248

KEYWORD

nonn,easy

AUTHOR

Joerg Arndt, Jun 07 2012

STATUS

approved

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