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

0,2

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)

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A022839, A276863, A276881.

Sequence in context: A330115 A189513 A194146 * A184906 A186156 A211267

Adjacent sequences: A276851 A276852 A276853 * A276855 A276856 A276857

Keyword

nonn,easy

Author

Clark Kimberling, Sep 24 2016

Status

approved