A287264 - OEIS

A287264

Positions of 0 in A287263.

1, 3, 7, 9, 15, 18, 19, 21, 25, 27, 33, 36, 39, 42, 43, 45, 49, 52, 53, 55, 57, 59, 63, 65, 71, 74, 75, 77, 81, 83, 89, 92, 95, 98, 99, 101, 105, 108, 109, 111, 115, 118, 119, 121, 125, 128, 129, 131, 133, 135, 139, 141, 147, 150, 151, 153, 157, 160, 161

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OFFSET

1,2

COMMENTS

The sequence A287263 is the fixed point with prefix 0 of the morphism sigma := 0->0202, 1->110, 2->11, the square of the defining morphism 0->11, 1->02, 2->0. - Michel Dekking, Oct 09 2019

From Michel Dekking, Oct 09 2019: (Start)

The sequence of first differences of (a(n)) is a morphic sequence, i.e., the letter to letter image of a fixed point of a morphism tau.

The morphism tau is obtained as the derived morphism of the word 0 in A287263. The return words (i.e., the words in A287263 with prefix 0 and containing no 0's) are 0, 01, 011, 0211, 021111. We have

sigma(0) = 0202,

sigma(01) = 020211,

sigma(011) = 0202110110,

sigma(0211) = 020211110110,

sigma(021111) = 020211110110110110.

From this one can see, coding the return words by their lengths, that the morphism tau is given by

tau: 1 -> 22, 2 -> 24, 3 -> 2431, 4 -> 2631, 6 -> 263331.

Let x = 2426312426333... be the unique fixed point of tau. Then

a(n+1) - a(n) = x(n) for n = 1,2,...

(End)

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..12223