A275167 Pisano periods of A275124.

20, 60, 60, 40, 40, 60, 60, 60, 120, 140, 80, 120, 60, 120, 120, 100, 220, 60, 40, 60, 260, 120, 420, 140, 100, 240, 120, 120, 180, 120, 120, 180, 380, 120, 300, 180, 280, 240, 80, 240, 660, 60, 120, 60, 500, 240, 780, 120, 540, 120, 420, 420, 80, 360, 300, 200, 240, 620, 140, 120, 220, 60, 240, 180, 440, 120, 120, 120, 180, 1140, 520, 120

Offset

1,1

Links

Table of n, a(n) for n=1..72.

Formula

a(n) = A001175(A275124(n)).

Example

A275124(1) = 55, and PisanoPeriod(55) = 20, etc.

Prog

(JavaScript)
let bases = [],
    Fs = [],
    Ls = [],
    agrees = [],
    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;
    }
    Fs[base] = fibs.length;
    Ls[base] = lucas.length;
    if (fibs.length != lucas.length)
        bases.push(base);
    //console.log('F', fibs.join(', '), 'L:', lucas.join(', '));
}
for (let i = 1; i <= baselimit/5; i++) {
    if (!bases.includes(i * 5)) {
        agrees.push(Fs[i * 5]);
    }
}
console.log(agrees.join(', '));

Crossrefs

Cf. A001175, A275124.

Sequence in context: A229536 A220013 A220046 * A344200 A163761 A154072

Adjacent sequences: A275164 A275165 A275166 * A275168 A275169 A275170

Keyword

nonn

Author

Dan Dart, Jul 18 2016

Status

approved