

A223488


Number of distinct residues in the Lucas sequence mod the nth 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
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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.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


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 A054426
Adjacent sequences: A223485 A223486 A223487 * A223489 A223490 A223491


KEYWORD

nonn


AUTHOR

Casey Mongoven, Mar 20 2013


STATUS

approved



