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 A275167 Pisano periods of A275124. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 26 12:54 EST 2024. Contains 370352 sequences. (Running on oeis4.)