A118287 A fractal transform of the Lucas numbers: define a(1)=1, then if L(n)A000032(n).

1, 2, 1, 3, 6, 5, 6, 10, 9, 10, 8, 17, 16, 17, 15, 12, 13, 12, 28, 27, 28, 26, 23, 24, 23, 19, 20, 19, 21, 46, 45, 46, 44, 41, 42, 41, 37, 38, 37, 39, 30, 31, 30, 32, 35, 34, 35, 75, 74, 75, 73, 70, 71, 70, 66, 67, 66, 68, 59, 60, 59, 61, 64, 63, 64, 48, 49, 48, 50, 53, 52, 53

Offset: 1

Author

Casey Mongoven, Apr 22 2006

Keywords

• nonn

Comments

From Jeffrey Shallit, Jan 01 2024: (Start)

No integer appears three times or more in this sequence.

If an integer appears twice, it appears as a(n) and a(n-2) for some n.

a(n) = a(n-2) if and only if n belongs to A003231. (observation of Benoit Cloitre)

All these and more properties can be proved using the synchronized Fibonacci automaton for a(n), which has 102 states. (End)

Links

• Benoit Cloitre and Jeffrey Shallit, Some Fibonacci-Related Sequences, arXiv:2312.11706 [math.CO], 2023-2024.

Crossrefs

Cf. A105774, A105669, A000032, A003231.