A285678 Positions of 0 in A285677.

1, 6, 8, 13, 15, 18, 20, 25, 27, 32, 34, 37, 39, 44, 46, 49, 51, 56, 58, 63, 65, 68, 70, 75, 77, 82, 84, 87, 89, 94, 96, 99, 101, 106, 108, 113, 115, 118, 120, 125, 127, 130, 132, 137, 139, 144, 146, 149, 151, 156, 158, 163, 165, 168, 170, 175, 177, 180, 182

Offset: 1

Author

Clark Kimberling, May 11 2017

Keywords

• nonn
• easy

Comments

A 3-way partition of the positive integers, by positions of 0, 1, 2 in A285677:

A285678: positions of 0; slope t = (4+sqrt(5))/2;

A182761: positions of 1; slope u = (7-sqrt(5))/2;

A285679: 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 {2,3,4,5} for n>=2.

Links

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

Crossrefs

Cf. A003849, A284620, A285678, A182761, A285679.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] ; (* A003849 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0010" -> "2"}]
st = ToCharacterCode[w1] - 48; (* A285677 *)
Flatten[Position[st, 0]];  (* A285678 *)
Flatten[Position[st, 1]];  (* A182761 *)
Flatten[Position[st, 2]];  (* A285679 *)