A339052 Odd bisection of the infinite Fibonacci word A096270.

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

Offset

0

Links

A.H.M. Smeets, Table of n, a(n) for n = 0..20000

Formula

a(n) = [(2n+2)r] - [(2n+1)r] - 1, where [ ] = floor and r = golden ratio (A001622).

a(n) = A005206(2*n+1) - A005206(2*n) = A001961(n+1) - A001965(n). - Peter Bala, Aug 09 2022

Example

A096270 = (0,1,0,1,1,0,1,0,1,1,0,1,1,.. ), so that
A339051 = (0,0,1,1,1,0,...), the even bisection.
A339052 = (1,1,0,0,1,1,...), the odd bisection.

Mathematica

r = (1 + Sqrt[5])/2; z = 200;
Table[Floor[(2 n + 1) r] - Floor[2 n r] - 1, {n, 0, Floor[z/2]}] (*A339051*)
Table[Floor[(2 n + 2) r] - Floor[(2 n + 1) r] - 1, {n, 0, Floor[z/2]}] (*A339052*)

Crossrefs

Cf. A001622, A001961, A001965, A005206, A096270, A339051, A339053, A339054.

Sequence in context: A128130 A133872 A286903 * A284490 A284505 A285661

Adjacent sequences: A339049 A339050 A339051 * A339053 A339054 A339055

Keyword

nonn,easy

Author

Clark Kimberling, Dec 08 2020

Status

approved