A110012 a(n) = n - F(F(n)) where F(x)=floor(sqrt(2)*floor(x/sqrt(2))).

1, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2

Offset

1,2

Comments

To built the sequence start from the infinite binary word b(k)=floor(k*(sqrt(2)-1))-floor((k-1)*(sqrt(2)-1)) for k>=1 giving 0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,... Then replace each 0 by the block {2,3,3} and each 1 by the block {2,2,3,3}. Append the initial string {1,2}.

References

B. Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005

Links

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

Mathematica

F[x_] := Floor[Sqrt[2]*Floor[x/Sqrt[2]]]; Table[n - F[F[n]], {n, 1, 100}] (* G. C. Greubel, Oct 02 2018 *)

Prog

(PARI) F(x)=floor(sqrt(2)*floor(x/sqrt(2)));
a(n)=n-F(F(n))

Crossrefs

Cf. A003842 (case a(n)=n-floor(phi*floor(phi^-1*n)), A006337.

Sequence in context: A081844 A233549 A334475 * A233542 A245908 A023514

Adjacent sequences: A110009 A110010 A110011 * A110013 A110014 A110015

Keyword

nonn

Author

Benoit Cloitre, Sep 02 2005

Status

approved