A275167 - OEIS

%I #10 Jun 23 2022 20:33:58

%S 20,60,60,40,40,60,60,60,120,140,80,120,60,120,120,100,220,60,40,60,

%T 260,120,420,140,100,240,120,120,180,120,120,180,380,120,300,180,280,

%U 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

%N Pisano periods of A275124.

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

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

%o (JavaScript)

%o let bases = [],

%o     Fs = [],

%o     Ls = [],

%o     agrees = [],

%o     baselimit = 2000;

%o for (let base = 2; base <= baselimit; base++) {

%o     let fibs = [1 % base,1 % base],

%o         lucas = [2 % base,1 % base],

%o         repeatingf = false,

%o         repeatingl = false;

%o     while (!repeatingf) {

%o         fibs.push((fibs[fibs.length - 2] + fibs[fibs.length - 1]) % base);

%o         if (1 == fibs[fibs.length - 2] &&

%o             0 == fibs[fibs.length - 1])

%o             repeatingf = true;

%o     }

%o     while (!repeatingl) {

%o         lucas.push((lucas[lucas.length - 2] + lucas[lucas.length - 1]) % base);

%o         if ((lucas[0] == (lucas[lucas.length - 2] + lucas[lucas.length - 1]) % base) &&

%o             (lucas[1] == (lucas[lucas.length - 2] + 2 *lucas[lucas.length - 1]) % base))

%o             repeatingl = true;

%o     }

%o     Fs[base] = fibs.length;

%o     Ls[base] = lucas.length;

%o     if (fibs.length != lucas.length)

%o         bases.push(base);

%o     //console.log('F', fibs.join(','), 'L:', lucas.join(','));

%o }

%o for (let i = 1; i <= baselimit/5; i++) {

%o     if (!bases.includes(i * 5)) {

%o         agrees.push(Fs[i * 5]);

%o     }

%o }

%o console.log(agrees.join(','));

%Y Cf. A001175, A275124.

%K nonn

%O 1,1

%A _Dan Dart_, Jul 18 2016