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A213247 Number of nonzero elements in GF(2^n) that are 11th powers. 8
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 (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, 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

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Last modified February 23 06:10 EST 2020. Contains 332159 sequences. (Running on oeis4.)