A285250 - OEIS

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A285250

Positions of 0 in A285249; complement of A285251.

1, 3, 6, 8, 9, 11, 14, 15, 17, 19, 21, 24, 26, 27, 29, 32, 33, 35, 38, 39, 41, 44, 45, 47, 49, 51, 54, 56, 57, 59, 62, 63, 65, 67, 69, 72, 73, 75, 78, 80, 81, 83, 86, 87, 89, 91, 93, 96, 98, 99, 101, 104, 105, 107, 110, 111, 113, 116, 117, 119, 121, 123, 126

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OFFSET

1,2

COMMENTS

Conjecture: 2n - a(n) is in {0,1} for n>=1.

Proof of this conjecture: Let (b(n))=A285249. Then clearly b(2n-1)b(2n)=01 or 10 for n=1,2,...So at time 2n you have seen n zeroes in the sequence b. The last of these must have occurred at time 2n or at time 2n-1, so either 2n-a(n)=0 or 2n-a(n)=1. - Michel Dekking, Jul 31 2017

LINKS

Table of n, a(n) for n=1..63.

EXAMPLE

As a word, A285249 = 010110100101..., in which 0 is in positions 1,3,6,8,9,11,14,...

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 1, 0, 1}}] &, {0}, 12]; (* A285249 *)

Flatten[Position[s, 0]]; (* A285250 *)

Flatten[Position[s, 1]]; (* A285251 *)

CROSSREFS

Cf. A285249, A285251, A285252.

Sequence in context: A335155 A231005 A231010 * A188469 A005652 A047401

Adjacent sequences: A285247 A285248 A285249 * A285251 A285252 A285253

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 23 2017

STATUS

approved