A284895 Positions of 1 in A284893; complement of A284894.

2, 4, 5, 6, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 24, 25, 26, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 72, 73, 74, 76, 78, 79, 80, 82, 83, 84, 86, 87, 88, 90, 92, 93, 94

Offset

1,1

Comments

Conjecture: 0 < a(n) - n*sqrt(2) < 1 for n >= 1.

The conjecture is false, since a(2) - 2*sqrt(2) = 4-2.828... > 1.17. Presumably the new conjecture is 0 < a(n) - n*sqrt(2) < 2 for n >= 1. - Michel Dekking, Jan 16 2018

This type of behavior typically occurs for Beatty sequences. However, {a(n)} is not a Beatty sequence, since the sequence of first differences {d(n)} of {a(n)} is not Sturmian: in d = 2,1,1,2,2,1,2,1,... there occur 5 words of length 3. One has d = A298231. - Michel Dekking, Jan 16 2018

Links

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

Example

As a word, A284893 = 010111010..., in which 0 is in positions 1,3,7,9,...

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0, 1, 1, 1}}] &, {0}, 6] (* A284893 *)
Flatten[Position[s, 0]]  (* A284894 *)
Flatten[Position[s, 1]]  (* A284895 *)

Crossrefs

Cf. A284893, A284895, A298231.

Sequence in context: A115836 A176554 A366322 * A285354 A050505 A340932

Adjacent sequences: A284892 A284893 A284894 * A284896 A284897 A284898

Keyword

nonn,easy

Author

Clark Kimberling, Apr 16 2017

Status

approved