OFFSET
1,1
COMMENTS
This is the Beatty sequence for tau_prime = 2.191487883953118747061354268227517294...,
defined by 1/tau + 1/tau_prime = 1.
Differs from A172278 at n = 162, 209, 256, 303, 324, ...
Note that Beatty sequences do not normally include 0 - see the classic pair A000201, A001950. - N. J. A. Sloane, Oct 19 2018
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..1000
Wikipedia, Beatty Sequence
FORMULA
a(n) = floor(n*tau_prime), with tau_prime = tau/(tau - 1), where tau is the tribonacci constant A058265.
tau_prime = (1 + (19 + 3*sqrt(33))^(1/3) + (19 - 3*sqrt(33))^(1/3)) / (-2 + (19 + 3*sqrt(33))^(1/3) + (19 - 3*sqrt(33))^(1/3)). - Wolfdieter Lang, Sep 08 2018
EXAMPLE
Comments from Wolfdieter Lang, Sep 08 2018 (Start):
n: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
A158919: 1 3 5 7 9 11 12 14 16 18 20 22 23 25 27 29 31 33 34 36 ...
A276383: 2 4 6 8 10 13 15 17 19 21 24 26 28 30 32 35 37 39 41 43 ...
--------------------------------------------------------------------
The complementary sequences AT, BT and CT begin:
n: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
AT: 1 5 8 12 14 18 21 25 29 32 36 38 42 45 49 52 56 58 62 65 ...
BT: 0 2 4 6 7 9 11 13 15 17 19 20 22 24 26 28 30 31 33 35 ...
CT: 3 10 16 23 27 34 40 47 54 60 67 71 78 84 91 97 104 108 115 121 ...
(End)
MAPLE
A276383 := proc(n)
Tau := (1/3)*(1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3));
taupr := 1/(1-1/Tau) ;
floor(n*taupr) ;
end proc: # R. J. Mathar, Sep 04 2016
a:=proc(n) local s, t; t:=evalf(solve(x^3-x^2-x-1=0, x), 120)[1]; s:=t/(t-1); floor(n*s) end; seq(a(n), n=0..70); # Muniru A Asiru, Oct 16 2018
CROSSREFS
Similar to but strictly different from A172278.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 02 2016
EXTENSIONS
Edited by N. J. A. Sloane, Oct 19 2018 at the suggestion of Georg Fischer
STATUS
approved