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A223488 Number of distinct residues in the Lucas sequence mod the n-th prime. 1

%I

%S 2,3,4,7,7,12,16,12,19,10,19,28,19,33,15,44,37,28,51,44,56,49,63,24,

%T 80,35,79,33,48,40,97,82,100,33,72,37,124,123,127,124,112,62,119,144,

%U 148,16,30,169,171,80,28,149,103,157,196,85,120,169,204,27,213,212

%N Number of distinct residues in the Lucas sequence mod the n-th prime.

%C The Lucas numbers mod n for any n are periodic; see A106291 for period lengths.

%D V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers. Houghton, Boston, MA, 1969.

%H T. D. Noe, <a href="/A223488/b223488.txt">Table of n, a(n) for n = 1..1000</a>

%e The 5th prime number is 11. The Lucas sequence mod 11 is {2,1,3,4,7,0,7,7,3,10,2,1,3,...} - a periodic sequence. There are 7 distinct residues in this sequence, namely {0,1,2,3,4,7,10}. So a(5) = 7.

%t pisano[n_] := Module[{a = {2, 1}, a0, k = 0, s}, If[n == 1, 1, a0 = a; Reap[While[k++; s = Mod[Plus @@ a, n]; Sow[s]; a[[1]] = a[[2]]; a[[2]] = s; a != a0]][[2, 1]]]]; Join[{2}, Table[u = Union[pisano[n]]; Length[u], {n, Prime[Range[2, 100]]}]] (* _T. D. Noe_, Mar 22 2013 *)

%Y Cf. A137750.

%K nonn

%O 1,1

%A _Casey Mongoven_, Mar 20 2013

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Last modified August 1 02:28 EDT 2021. Contains 346377 sequences. (Running on oeis4.)