

A104480


Numbers n such that the period length P(n) of the Fibonacci sequence modulo n is a perfect square.


0



1, 7, 17, 21, 25, 34, 68, 97, 119, 127, 133, 136, 152, 175, 189, 238, 266, 275, 323, 337, 343, 357, 378, 381, 391, 399, 425, 437, 475, 476, 505, 525, 532, 544, 577, 608, 621, 625, 646, 647, 679, 707, 714, 749, 755, 756, 782, 798, 850, 864, 874, 889, 950, 952
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

144 appears to be the most common perfect square.


LINKS

Table of n, a(n) for n=1..54.


EXAMPLE

Let P(n) be the period length of the modulo n Fibonacci sequence (also called the Pisano period). Then {P(n)}=1,3,8,6,20,24,16,12,... and a(2)=7 because the second perfect square in {P(n)} occurs when n=7.


MATHEMATICA

t = {1}; Do[a = {1, 0}; a0 = a; k = 0; While[k++; s = Mod[Plus @@ a, n]; a = RotateLeft[a]; a[[2]] = s; a != a0]; If[IntegerQ[Sqrt[k]], AppendTo[t, n]], {n, 2, 1000}]; t (* T. D. Noe, Aug 08 2012 *)


CROSSREFS

Cf. A001175.
Sequence in context: A180641 A234095 A287182 * A053746 A327830 A144695
Adjacent sequences: A104477 A104478 A104479 * A104481 A104482 A104483


KEYWORD

nonn


AUTHOR

William C. Brown (wcbrow00(AT)centre.edu), Apr 18 2005


STATUS

approved



