

A223487


Number of missing residues in Lucas sequence mod n.


3



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, 10, 16, 14, 22, 21, 9, 25, 15, 30, 22, 16, 10, 24, 28, 25, 32, 31, 12, 26, 20, 16, 9, 25, 39, 28, 28, 38, 22, 42, 33, 41, 30, 22, 49, 32, 16, 42, 36, 44, 27, 55
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,8


COMMENTS

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


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525532.


MATHEMATICA

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 *)


CROSSREFS

Cf. A118965.
Sequence in context: A182256 A164993 A305572 * A226911 A291956 A023987
Adjacent sequences: A223484 A223485 A223486 * A223488 A223489 A223490


KEYWORD

nonn


AUTHOR

Casey Mongoven, Mar 20 2013


STATUS

approved



