A339825 Odd bisection of the infinite Fibonacci word A003849.

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

Offset

0

Links

Table of n, a(n) for n=0..85.

Formula

a(n) = 2 - [(2n+3)r] - [(2n+2)r], where [ ] = floor and r = golden ratio (A001622).

Example

A003849 = (0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0,.. ), so that
A339824 = (0, 0, 1, 1, 0, 0, 1,...), the even bisection.
A339825 = (1, 0, 0, 0, 1, 0, 0,...), the odd bisection.

Mathematica

r = (1 + Sqrt[5])/2; z = 300;
f[n_] := 2 - Floor[(n + 2) r] + Floor[(n + 1) r]; (*A003849*)
Table[2 - Floor[(2 n + 2) r] + Floor[(2 n + 1) r], {n, 0, Floor[z/2]}] (*A339824 *)
Table[2 - Floor[(2 n + 3) r] + Floor[(2 n + 2) r], {n, 0, Floor[z/2]}] (*A339825 *)

Crossrefs

Cf. A001622, A096270, A339824, A339826, A339827.

Sequence in context: A014017 A121262 A181923 * A290098 A102243 A173859

Adjacent sequences: A339822 A339823 A339824 * A339826 A339827 A339828

Keyword

nonn

Author

Clark Kimberling, Dec 19 2020

Status

approved