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A276854
Beatty sequence for 1 + sqrt(5).
6
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 24 2016
STATUS
approved