OFFSET
1,1
COMMENTS
m is on this list iff m does not have 1 or 4 zeros in the Fibonacci sequence modulo m.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Brennan Benfield and Oliver Lippard, Connecting Zeros in Pisano Periods to Prime Factors of K-Fibonacci Numbers, arXiv:2407.20048 [math.NT], 2024. See p. 2.
Brennan Benfield and Michelle Manes, The Fibonacci Sequence is Normal Base 10, arXiv:2202.08986 [math.NT], 2022.
M. Renault, Fibonacci sequence modulo m
PROG
(Haskell)
a053030 n = a053030_list !! (n-1)
a053030_list = filter ((== 2) . a001176) [1..]
-- Reinhard Zumkeller, Jan 17 2014
CROSSREFS
Let {x(n)} be a sequence defined by x(0) = 0, x(1) = 1, x(n+2) = m*x(n+1) + x(n). Let w(k) be the number of zeros in a fundamental period of {x(n)} modulo k.
| m=1 | m=2 | m=3
-----------------------------+----------+---------+---------
* and also A053032 U {2}
KEYWORD
nonn
AUTHOR
Henry Bottomley, Feb 23 2000
STATUS
approved