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!)
A106298 Period of the Lucas 5-step sequence A074048 mod prime(n). 5

%I #28 Mar 24 2024 07:57:50

%S 1,104,781,2801,16105,30941,88741,13032,12166,70728,190861,1926221,

%T 2896405,79506,736,8042221,102689,3720,20151120,2863280,546120,

%U 39449441,48030024,3690720,29509760,104060400,37516960,132316201,28231632,6384,86714880,2248090,3128

%N Period of the Lucas 5-step sequence A074048 mod prime(n).

%C This sequence is the same as the period of Fibonacci 5-step sequence (A106304) mod prime(n) except for n=1 and 109, which correspond to the primes 2 and 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. We have a(n) < prime(n) for the primes 2, 599 and A106281.

%H Chai Wah Wu, <a href="/A106298/b106298.txt">Table of n, a(n) for n = 1..82</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.

%F a(n) = A106297(prime(n)).

%t n=5; Table[p=Prime[i]; a=Join[Table[ -1, {n-1}], {n}]; 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, 40}]

%o (Python)

%o from itertools import count

%o from sympy import prime

%o def A106298(n):

%o a = b = (5%(p:=prime(n)),1%p,7%p,3%p,15%p)

%o s = sum(b) % p

%o for m in count(1):

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

%o if a == b:

%o return m # _Chai Wah Wu_, Feb 22-27 2022

%Y Cf. A106281 (primes p such that x^5-x^4-x^3-x^2-x-1 mod p has 5 distinct zeros), A106297.

%K nonn,changed

%O 1,2

%A _T. D. Noe_, May 02 2005

%E a(31)-a(33) from _Chai Wah Wu_, Feb 27 2022

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 March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)