



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
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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) = 42.828... > 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: A080653 A115836 A176554 * A285354 A050505 A047262
Adjacent sequences: A284892 A284893 A284894 * A284896 A284897 A284898


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Apr 16 2017


STATUS

approved



