A282162 Difference sequence of the upper Wythoff sequence, A001950, with 2 prepended.

2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3

Offset: 0

Author

Clark Kimberling, Feb 09 2017

Keywords

• nonn
• easy

Comments

Another version of the infinite Fibonacci word (see Formula). Start with 2, apply 2->23, 3->233, and take the limit.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001950, A001468, A076662.

Programs

Mathematica

r = GoldenRatio^2; Table[Floor[(n + 1) r] - Floor[n r], {n, 0, 120}]

Python

from math import isqrt
def A282162(n): return (n+3+isqrt(m:=5*(n+1)**2)>>1)-(n+isqrt(m-10*n-5)>>1) # Chai Wah Wu, May 05 2025

Formula

a(n) = 1 + A001468(n).