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A285681 Positions of 0 in A285680. 4
1, 3, 4, 6, 8, 9, 11, 13, 15, 16, 18, 20, 21, 23, 25, 27, 28, 30, 32, 34, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 71, 73, 75, 77, 78, 80, 82, 84, 85, 87, 89, 90, 92, 94, 96, 97, 99, 101, 102, 104, 106, 108, 109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A 3-way partition of the positive integers, by positions of 0, 1, 2 in A285680:

A285681: positions of 0; slope t = (15+sqrt(5))/10;

A285682: positions of 1; slope u = (4+sqrt(5);

A285683: positions of 2; slope v = (1+3*sqrt(5))/2;

where 1/t + 1/u + 1/v = 1.  Conjecture:  a(n) - a(n-1) is in {1,2} for n>=2.

LINKS

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

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] ; (* A003849 *)

w = StringJoin[Map[ToString, s]]

w1 = StringReplace[w, {"1010" -> "2"}]

st = ToCharacterCode[w1] - 48; (* A285680 *)

Flatten[Position[st, 0]];  (* A285681 *)

Flatten[Position[st, 1]];  (* A285682 *)

Flatten[Position[st, 2]];  (* A285683 *)

CROSSREFS

Cf. A003849, A285680, A258682, A285683.

Sequence in context: A047206 A187474 A081031 * A133280 A280762 A138097

Adjacent sequences:  A285678 A285679 A285680 * A285682 A285683 A285684

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 11 2017

STATUS

approved

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)