A287264 - OEIS

%I #22 Oct 14 2019 00:30:05

%S 1,3,7,9,15,18,19,21,25,27,33,36,39,42,43,45,49,52,53,55,57,59,63,65,

%T 71,74,75,77,81,83,89,92,95,98,99,101,105,108,109,111,115,118,119,121,

%U 125,128,129,131,133,135,139,141,147,150,151,153,157,160,161

%N Positions of 0 in A287263.

%C 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

%C From _Michel Dekking_, Oct 09 2019: (Start)

%C 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.

%C 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

%C     sigma(0) = 0202,

%C     sigma(01) = 020211,

%C     sigma(011) = 0202110110,

%C     sigma(0211) = 020211110110,

%C     sigma(021111) = 020211110110110110.

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

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

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

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

%C (End)

%H Clark Kimberling, <a href="/A287264/b287264.txt">Table of n, a(n) for n = 1..12223</a>

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 2}, 2 -> 0}] &, {0}, 10] (* A287263 *)

%t Flatten[Position[s, 0]] (* A287264 *)

%t Flatten[Position[s, 1]] (* A287265 *)

%t Flatten[Position[s, 2]] (* A287266 *)

%Y Cf. A287264, A287265, A287266.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 24 2017