OFFSET
1,1
LINKS
Patrick Flanagan, Marc S. Renault, and Josh Updike, Symmetries of Fibonacci Points, Mod m, Fibonacci Quart. 53 (2015), no. 1, 34-41. See p. 7. (Is this the same sequence?)
EXAMPLE
55 is the first multiple of 5 where the Pisano period (Fibonacci) of n = 55 and the Pisano period (Lucas) of n = 55 agree (this is in this case 20).
PROG
(JavaScript)
let bases = [],
basesd = [],
baselimit = 2000;
for (let base = 2; base <= baselimit; base++) {
let fibs = [1 % base, 1 % base],
lucas = [2 % base, 1 % base],
repeatingf = false,
repeatingl = false;
while (!repeatingf) {
fibs.push((fibs[fibs.length - 2] + fibs[fibs.length - 1]) % base);
if (1 == fibs[fibs.length - 2] &&
0 == fibs[fibs.length - 1])
repeatingf = true;
}
while (!repeatingl) {
lucas.push((lucas[lucas.length - 2] + lucas[lucas.length - 1]) % base);
if ((lucas[0] == (lucas[lucas.length - 2] + lucas[lucas.length - 1]) % base) &&
(lucas[1] == (lucas[lucas.length - 2] + 2 *lucas[lucas.length - 1]) % base))
repeatingl = true;
}
if (fibs.length != lucas.length)
bases.push(base);
}
for (let i = 1; i <= baselimit/5; i++) {
if (!bases.includes(i * 5)) basesd.push(i * 5);
}
console.log(basesd.join(', '));
CROSSREFS
KEYWORD
nonn
AUTHOR
Dan Dart, Jul 18 2016
STATUS
approved