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A110012
a(n) = n - F(F(n)) where F(x)=floor(sqrt(2)*floor(x/sqrt(2))).
1
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
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 A375802 A245908
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Sep 02 2005
STATUS
approved