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%I
%S 80,40,20,10,5,43,62,31,56,28,14,7,44,22,11,46,23,52,26,13,47,64,32,
%T 16,8,4,2,1,41,61,71,76,38,19,50,25,53,67,74,37,59,70,35,58,29,55,68,
%U 34,17,49,65,73,77,79,80,40,20,10,5,43,62,31,56,28,14,7,44
%N A sequence with period length 54; the companion of x(n) = A239130(n), the smallest positive solution of 3^4*x - 2^n*y = 1 for n >= 0.
%C The first 54 = phi(3^4) values of a(n) = y0(4, n) have been given, with phi(n) = A000010(n). They give a permutation of the smallest positive restricted residue class modulo 3^4.
%C The companion sequence is x0(4, n) = x(n) = A239130(n), n >= 0.
%C One could give a lengthy G.f.
%H Vincenzo Librandi, <a href="/A239131/b239131.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = y0(4, n) == ((3^4 + 1)/2)^(n + 3^3) (mod 3^4), n >= 0.
%F a(n + 54) = a(n), n >= 0.
%e a(0) = 41^27 (mod 81) = 80.
%t Table[Mod[41^(n + 27), 81], {n, 0, 100}] (* _Vincenzo Librandi_, Mar 23 2014 *)
%t PowerMod[41,Range[0,100]+27,81] (* _Harvey P. Dale_, Dec 04 2018 *)
%o (MAGMA) [41^(n+27) mod 81: n in [0..80]]; // _Vincenzo Librandi_, Mar 23 2014
%Y Cf. A239130.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Mar 22 2014
%E More terms from _Vincenzo Librandi_, Mar 23 2014
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