login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A275124 Multiples of 5 where Pisano periods of Fibonacci numbers A001175 and Lucas numbers A106291 agree. 1
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.

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: A044525 A118151 A277273 * A282768 A217429 A154031

Adjacent sequences:  A275121 A275122 A275123 * A275125 A275126 A275127

KEYWORD

nonn

AUTHOR

Kathie Dart, Jul 18 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified July 25 02:46 EDT 2017. Contains 289779 sequences.