A276854 Beatty sequence for 1 + sqrt(5).

0, 3, 6, 9, 12, 16, 19, 22, 25, 29, 32, 35, 38, 42, 45, 48, 51, 55, 58, 61, 64, 67, 71, 74, 77, 80, 84, 87, 90, 93, 97, 100, 103, 106, 110, 113, 116, 119, 122, 126, 129, 132, 135, 139, 142, 145, 148, 152, 155, 158, 161, 165, 168, 171, 174, 177, 181, 184, 187

Offset: 0

Author

Clark Kimberling, Sep 24 2016

Keywords

• nonn
• easy

Comments

A bisection of the lower Wythoff sequence, A000201.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..10000
• N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Crossrefs

Cf. A022839, A276863, A276881.

Programs

Mathematica

z = 500; r = 1+Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}] (* A276854 *)

Python

from sympy import integer_nthroot
def A276854(n): return n+integer_nthroot(5*n**2,2)[0] # Chai Wah Wu, Mar 16 2021

Formula

a(n) = floor(n*(1 + sqrt(5))).