A187976 a(n) = [nr+kr]-[nr]-[kr], where r=sqrt(2), k=6, [ ]=floor.

0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0

Offset

1

Comments

See A187950.

The frequency of 1 in (a(n)) is equal to 6*sqrt(2)-8. This can be determined from the 6-block substitution sigma-hat of sigma given by sigma(1)=12, sigma(2)=121, which generates A006337. - Michel Dekking, Jan 24 2017

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

F. Michel Dekking, Morphisms, Symbolic Sequences, and Their Standard Forms, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.

Formula

a(n) = [(n+6)*r] - [n*r] - [6*r], where r=sqrt(2).

Mathematica

r=2^(1/2);
seqA=Table[Floor[(n+6)r]-Floor[n*r]-Floor[6r], {n, 1, 220}]   (* A187976 *)
Flatten[Position[seqA, 0] ]   (* A187977 *)
Flatten[Position[seqA, 1] ]   (* A187978 *)

Prog

(PARI) for(n=1, 30, print1(floor((n+6)*sqrt(2)) - floor(n*sqrt(2)) - floor(6*sqrt(2)), ", ")) \\  G. C. Greubel, Jan 31 2018
(Magma) [Floor((n+6)*Sqrt(2)) - Floor(n*Sqrt(2)) - Floor(6*Sqrt(2)): n in [1..30]]; // G. C. Greubel, Jan 31 2018

Crossrefs

Cf. A187977, A187978.

Sequence in context: A163538 A267188 A154104 * A197879 A296657 A082848

Adjacent sequences: A187973 A187974 A187975 * A187977 A187978 A187979

Keyword

nonn

Author

Clark Kimberling, Mar 17 2011

Status

approved