A285682 Positions of 1 in A285680.

2, 7, 14, 19, 26, 33, 38, 45, 50, 57, 64, 69, 76, 83, 88, 95, 100, 107, 114, 119, 126, 131, 138, 145, 150, 157, 164, 169, 176, 181, 188, 195, 200, 207, 214, 219, 226, 231, 238, 245, 250, 257, 262, 269, 276, 281, 288, 295, 300, 307, 312, 319, 326, 331, 338

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 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 {5,7} for n >= 2.

Links

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

Crossrefs

Cf. A003849, A285680, A285681, A285683.

Programs

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 *)