A213245 Number of nonzero elements in GF(2^n) that are 7th powers.
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
Offset: 1
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).
Crossrefs
Programs
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Magma
[(2^n - 1) / GCD (2^n - 1, 7): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013
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Maple
A213245:=n->(2^n-1)/gcd(2^n-1,7): seq(A213245(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014
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Mathematica
Table[(2^n - 1)/GCD[2^n - 1, 7], {n, 60}] (* Vincenzo Librandi, Mar 16 2013 *) -
PARI
a(n)=(2^n-1)/gcd(2^n-1,7) \\ Edward Jiang, Sep 04 2014
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)