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A285250
Positions of 0 in A285249; complement of A285251.
11
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
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 23 2017
STATUS
approved