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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2017
STATUS
approved