OFFSET
1,5
COMMENTS
LINKS
B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.8.5.
EXAMPLE
The sequence 2,1,3,4,2,1 is the sequence of Lucas numbers modulo 5. Lucas numbers are never divisible by 5. The 4 pairs (2,1), (1,3), (3,4), (4,2) are the only pairs that can generate a sequence modulo 5 that doesn't contain zeros. Thus, a(5) = 4.
Any Fibonacci like sequence contains elements divisible by 2, 3, or 4. Thus, a(2) = a(3) = a(4) = 0.
MATHEMATICA
fibLike[list_] := Append[list, list[[-1]] + list[[-2]]]; Table[Count[Flatten[Table[Count[Nest[fibLike, {n, m}, k^2]/k, _Integer], {n, k-1}, {m, k-1}]], 0], {k, 70}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Brandon Avila and Tanya Khovanova, Nov 22 2013
STATUS
approved