OFFSET
1,1
COMMENTS
From Gandhar Joshi, Jan 25 2025: (Start)
F(n) is the n-th Fibonacci number.
Conjecture: for n>0,
1. a(F(2n))=F(4n)-1; a(F(2n+1))=F(2n+3)-2.
2. a(F(6n)/2)=F(6n+3)/2-1; a(F(6n-3)/2)=F(6n)/2-2. (End)
LINKS
Gandhar Joshi, Table of n, a(n) for n = 1..1973
Ibai Aedo, U. Grimm, Y. Nagai, and P. Staynova, Monochromatic arithmetic progressions in binary Thue-Morse-like words, Theor. Comput. Sci., 934 (2022), 65-80.
Gandhar Joshi and D. Rust, Monochromatic arithmetic progressions in the Fibonacci word, arXiv:2501.05830 [math.DS], 2025. See p.12.
EXAMPLE
PROG
(Walnut)
# In the following line, replace every n with the desired constant difference, and every q with the longest MAP length for difference n given by A339949(n).
def f_n_map "?msd_fib Ak (k<q) => F[i]=F[i+n*k] & Aj (j<i) => ~(Ak (k<q) => F[j]=F[j+n*k])";
# Gandhar Joshi, Jan 25 2025
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Gandhar Joshi, Jul 31 2023
STATUS
approved