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 Number.
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
KEYWORD
nonn
AUTHOR
T. D. Noe, May 02 2005
STATUS
approved