A118287 A fractal transform of the Lucas numbers: define a(1)=1, then if L(n)<k<=L(n+1) a(k) = L(n+1) - a(k-L(n)) where 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

1,2

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

Table of n, a(n) for n=1..72.

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

Crossrefs

Cf. A105774, A105669, A000032, A003231.

Sequence in context: A205840 A171084 A332318 * A024930 A121966 A349980

Adjacent sequences: A118284 A118285 A118286 * A118288 A118289 A118290

Keyword

nonn

Author

Casey Mongoven, Apr 22 2006

Status

approved