A372846 a(n) is the number of states in the smallest deterministic finite automaton that accepts the Zeckendorf representation of i and n*i, in parallel, for all integers i>=0.

2, 10, 23, 40, 59, 85, 114, 146, 181, 224, 269, 318, 371, 429, 489, 552, 621, 695, 771, 850, 935, 1024, 1115, 1213, 1314, 1418, 1525, 1640, 1757, 1878, 2003, 2132, 2264, 2399, 2541, 2686, 2834, 2985, 3143, 3303, 3467, 3636, 3809, 3985, 4164, 4350, 4539, 4731

Offset

1,1

Comments

Conjecture: a(n) <= 2*n^2 + g^2*n + 1, where g = (1+sqrt(5))/2.

Links

Table of n, a(n) for n=1..48.

Delaram Moradi, State Complexity of Linear Relations and Linear Subsequences of Automatic Sequences, Master's Thesis, Univ. Waterloo (Ontario, Canada, 2026). See p. 67.

Delaram Moradi, Narad Rampersad, and Jeffrey Shallit, Complexity of Linear Subsequences of Fibonacci-Automatic Sequences, arXiv:2603.21645 [cs.FL], 2026. See p. 12.

Crossrefs

Cf. A001622, A014417.

Sequence in context: A333703 A120548 A284360 * A255606 A293403 A316451

Adjacent sequences: A372843 A372844 A372845 * A372847 A372848 A372849

Keyword

nonn

Author

Jeffrey Shallit, Jul 04 2024

Status

approved