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A285968 Positions of 1 in A285966; complement of A285967. 3
2, 4, 7, 10, 12, 14, 17, 19, 22, 24, 27, 30, 32, 35, 37, 40, 42, 44, 47, 50, 52, 54, 57, 59, 62, 64, 67, 69, 71, 74, 77, 79, 82, 84, 87, 90, 92, 94, 97, 99, 102, 104, 107, 110, 112, 115, 117, 120, 122, 124, 127, 130, 132, 135, 137, 140, 143, 145, 147, 150 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: a(n)/n -> 5/2.

From Michel Dekking, Mar 15 2019: (Start)

Proof of this conjecture:  it is equivalent to prove that the frequency of 1 in A285966 exists and equals 2/5.

This follows from my characterization of A285966 as a morphic sequence.

The incidence matrix of that morphism has Perron-Frobenius eigenvalue 2, with right eigenvector (1,1,2,1). It follows that the letters 2 and 4 in the fixed point of the morphism have both frequency 1/5. As these are exactly the letters that are mapped to 1 in A285966, the letter 1 has frequency 2/5 in A285966.

(End)

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

EXAMPLE

As a word, A285966 = 01010010010101001010010..., in which 1 is in positions 2,4,7,10,12,...

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* Thue-Morse, A010060 *)

w = StringJoin[Map[ToString, s]]

w1 = StringReplace[w, {"11" -> "1"}]

st = ToCharacterCode[w1] - 48 (* A285966 *)

Flatten[Position[st, 0]]  (* A285967 *)

Flatten[Position[st, 1]]  (* A285968 *)

CROSSREFS

Cf. A010060, A285966, A285967.

Sequence in context: A288482 A177093 A164903 * A218772 A057843 A047539

Adjacent sequences:  A285965 A285966 A285967 * A285969 A285970 A285971

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 06 2017

STATUS

approved

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)