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

Author

Dan Dart, Jul 18 2016

Keywords

• nonn

Examples

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

Crossrefs

Cf. A001175, A275124.

Programs

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(','));

Formula

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