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

%I A213247 #33 Jan 09 2025 18:11:18
%S A213247 1,3,7,15,31,63,127,255,511,93,2047,4095,8191,16383,32767,65535,
%T A213247 131071,262143,524287,95325,2097151,4194303,8388607,16777215,33554431,
%U A213247 67108863,134217727,268435455,536870911,97612893,2147483647,4294967295,8589934591,17179869183,34359738367,68719476735
%N A213247 Number of nonzero elements in GF(2^n) that are 11th powers.
%H A213247 Vincenzo Librandi, <a href="/A213247/b213247.txt">Table of n, a(n) for n = 1..1000</a>
%H A213247 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1025, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1024).
%F A213247 a(n) = M / GCD( M, 11 ) where M=2^n-1.
%F A213247 From _Colin Barker_, Aug 24 2014: (Start)
%F A213247 a(n) = 1025*a(n-10)-1024*a(n-20).
%F A213247 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).
%F A213247 (End)
%F A213247 a(n) = (2^n - 1)/11 if n is divisible by 10, 2^n - 1 otherwise. - _Robert Israel_, Aug 24 2014
%p A213247 A213247:=n->(2^n-1)/igcd(2^n-1,11): seq(A213247(n), n=1..40); # _Wesley Ivan Hurt_, Aug 24 2014
%t A213247 Table[(2^n - 1)/GCD[2^n - 1, 11], {n, 50}] (* _Vincenzo Librandi_, Mar 16 2013 *)
%o A213247 (Magma) [(2^n - 1) / GCD (2^n - 1, 11): n in [1..40]]; // _Vincenzo Librandi_, Mar 16 2013
%o A213247 (PARI) { for(n=1,36,if(n%10,a=2^n-1,a=(2^n-1)/11);print1(a,", ")) } \\ _K. Spage_, Aug 23 2014
%Y A213247 Cf. A213243 (cubes), A213244 (5th powers), A213245 (7th powers), A213246 (9th powers), A213248 (13th powers).
%K A213247 nonn
%O A213247 1,2
%A A213247 _Joerg Arndt_, Jun 07 2012