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A223488
Number of distinct residues in the Lucas sequence mod the n-th prime.
1
2, 3, 4, 7, 7, 12, 16, 12, 19, 10, 19, 28, 19, 33, 15, 44, 37, 28, 51, 44, 56, 49, 63, 24, 80, 35, 79, 33, 48, 40, 97, 82, 100, 33, 72, 37, 124, 123, 127, 124, 112, 62, 119, 144, 148, 16, 30, 169, 171, 80, 28, 149, 103, 157, 196, 85, 120, 169, 204, 27, 213, 212
OFFSET
1,1
COMMENTS
The Lucas numbers mod n for any n are periodic; see A106291 for period lengths.
REFERENCES
V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers. Houghton, Boston, MA, 1969.
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Cf. A137750.
Sequence in context: A239972 A162425 A217254 * A175686 A305563 A368037
KEYWORD
nonn
AUTHOR
Casey Mongoven, Mar 20 2013
STATUS
approved