A213248 Number of nonzero elements in GF(2^n) that are 13th powers.
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
Offset: 1
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4097, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4096).
Crossrefs
Programs
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Magma
[(2^n - 1) / GCD (2^n - 1, 13): n in [1..40]]; // Vincenzo Librandi, Mar 17 2013
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Maple
A213248:=n->(2^n-1)/gcd(2^n-1,13): seq(A213248(n), n=1..40); # Wesley Ivan Hurt, Aug 24 2014
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Mathematica
Table[(2^n - 1)/GCD[2^n - 1, 13], {n, 40}] (* Vincenzo Librandi, Mar 17 2013 *) -
PARI
a(n)=(2^n-1)/gcd(2^n-1,13) \\ Edward Jiang, Sep 04 2014
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)