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%I #10 Nov 19 2015 02:46:26
%S 0,0,0,0,1,0,0,2,0,2,4,2,1,0,8,5,1,7,7,10,8,8,4,10,13,2,0,8,19,16,12,
%T 10,16,14,22,21,9,25,15,30,22,16,10,24,28,25,32,31,12,26,20,16,9,25,
%U 39,28,28,38,22,42,33,41,30,22,49,32,16,42,36,44,27,55
%N Number of missing residues in Lucas sequence mod n.
%C The Lucas numbers mod n for any n are periodic - see A106291 for period lengths.
%H T. D. Noe, <a href="/A223487/b223487.txt">Table of n, a(n) for n = 1..1000</a>
%H D. D. Wall, <a href="http://www.jstor.org/stable/2309169">Fibonacci series modulo m</a>, Amer. Math. Monthly, 67 (1960), 525-532.
%t pisano[n_] := Module[{a = {2, 1}, a0, k = 0, s, t}, If[n == 1, 1, a0 = a; t = a; While[k++; s = Mod[Plus @@ a, n]; AppendTo[t, s]; a[[1]] = a[[2]]; a[[2]] = s; a != a0]; t]]; Join[{0, 0}, Table[u = Union[pisano[n]]; mx = Max[u]; Length[Complement[Range[0, mx], u]], {n, 3, 100}]] (* _T. D. Noe_, Mar 22 2013 *)
%Y Cf. A118965.
%K nonn
%O 1,8
%A _Casey Mongoven_, Mar 20 2013
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