login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A106303 Period of the Fibonacci 5-step sequence A001591 mod n. 9
1, 6, 104, 12, 781, 312, 2801, 24, 312, 4686, 16105, 312, 30941, 16806, 81224, 48, 88741, 312, 13032, 9372, 291304, 96630, 12166, 312, 3905, 185646, 936, 33612, 70728, 243672, 190861, 96, 1674920, 532446, 2187581, 312, 1926221, 13032 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence differs from the corresponding Lucas sequence (A106297) at all n that are multiples of 2 or 599 because 9584 is the discriminant of the characteristic polynomial x^5-x^4-x^3-x^2-x-1 and the prime factors of 9584 are 2 and 599.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..388

Eric Weisstein's World of Mathematics, Fibonacci n-Step

FORMULA

Let the prime factorization of n be p1^e1...pk^ek. Then a(n) = lcm(a(p1^e1), ..., a(pk^ek)).

Conjectures: a(5^k) = 781*5^(k-1) for k > 0. If a(p) != a(p^2) for p prime, then a(p^k) = p^(k-1)*a(p) for k > 0. - Chai Wah Wu, Feb 25 2022

MATHEMATICA

n=5; Table[p=i; a=Join[{1}, Table[0, {n-1}]] a=Mod[a, p]; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; a!=a0]; k, {i, 50}]

PROG

(Python)

from itertools import count

def A106303(n):

    a = b = (0, )*4+(1 % n, )

    s = 1 % n

    for m in count(1):

        b, s = b[1:] + (s, ), (s+s-b[0]) % n

        if a == b:

            return m # Chai Wah Wu, Feb 21-27 2022

CROSSREFS

Cf. A001591, A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1), A106297 (period of Lucas 5-step sequence mod n).

Sequence in context: A302911 A174481 A306205 * A157518 A001526 A295940

Adjacent sequences:  A106300 A106301 A106302 * A106304 A106305 A106306

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 16 22:37 EDT 2022. Contains 353724 sequences. (Running on oeis4.)