OFFSET
1,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
Aviezri S. Fraenkel, Jonathan Levitt, Michael Shimshoni, Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no.4, 335-345.
Eric Weisstein's World of Mathematics, Beatty Sequence.
FORMULA
a(n) = floor(n*(sqrt(3)+2)). - Michel Marcus, Jan 05 2015
For n >= 0, a(n) = 2n + largest integer m such that m^2 <= 3*n^2. - Chai Wah Wu, Oct 08 2016
From Miko Labalan, Dec 03 2016: (Start)
For n > 0, a(n) = 4*floor(n*(sqrt(3)-1)) + 3*floor(n*(2-sqrt(3))) + 3;
(End)
MAPLE
Digits := 60: A003512 := proc(n) trunc( evalf( n*(sqrt(3)+2) )); end;
MATHEMATICA
Table[Floor[n (Sqrt@ 3 + 2)], {n, 50}] (* Michael De Vlieger, Oct 08 2016 *)
PROG
(Python)
from gmpy2 import isqrt
def A003512(n):
return 2*n + int(isqrt(3*n**2)) # Chai Wah Wu, Oct 08 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved