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A213248 Number of nonzero elements in GF(2^n) that are 13th powers. 6
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 (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, 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: A043755 A105755 A043764 * A097002 A060152 A126646

Adjacent sequences:  A213245 A213246 A213247 * A213249 A213250 A213251

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jun 07 2012

STATUS

approved

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Last modified November 23 18:56 EST 2017. Contains 295128 sequences.