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 A275124 Multiples of 5 where Pisano periods of Fibonacci numbers A001175 and Lucas numbers A106291 agree. 3
 55, 110, 155, 165, 205, 220, 305, 310, 330, 355, 385, 410, 440, 465, 495, 505, 605, 610, 615, 620, 655, 660, 710, 715, 755, 770, 820, 880, 905, 915, 930, 935, 955, 990, 1010, 1045, 1065, 1085, 1155, 1205, 1210, 1220, 1230, 1240, 1255, 1265, 1310, 1320, 1355, 1395, 1420, 1430, 1435, 1485, 1510, 1515, 1540, 1555, 1595, 1640, 1655, 1705, 1760, 1810, 1815, 1830 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Multiples of 5 where A001175 and A106291 agree. See 1st comment of A106291. LINKS Table of n, a(n) for n=1..66. 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 Cf. A001175, A106291. Sequence in context: A323070 A118151 A277273 * A282768 A217429 A154031 Adjacent sequences: A275121 A275122 A275123 * A275125 A275126 A275127 KEYWORD nonn AUTHOR Dan Dart, Jul 18 2016 STATUS approved

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Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)