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A182778
Beatty sequence for 3 + sqrt(3).
4
4, 9, 14, 18, 23, 28, 33, 37, 42, 47, 52, 56, 61, 66, 70, 75, 80, 85, 89, 94, 99, 104, 108, 113, 118, 123, 127, 132, 137, 141, 146, 151, 156, 160, 165, 170, 175, 179, 184, 189, 194, 198, 203, 208, 212, 217, 222, 227, 231, 236, 241, 246, 250, 255
OFFSET
1,1
COMMENTS
Let u=2-sqrt(3) and v=1. Jointly rank {ju} and {kv} as in the first comment at A182760; a(n) is the position of n. A182778 is the complement of A182777.
LINKS
FORMULA
a(n) = floor(n*(3 + sqrt(3))).
From Miko Labalan, Dec 17 2016: (Start)
a(n) = 3n + A022838(n);
For n > 0, a(n) = 5*floor(n*(sqrt(3)-1)) + 4*floor(n*(2-sqrt(3))) + 4;
a(0) = 0, a(n) = a(n - 1) + A022838(n) - A022838(n - 1) + 3.
(End)
MATHEMATICA
Table[Floor[(3+Sqrt[3])*n], {n, 54}]
PROG
(Magma) [Floor(n*(3+Sqrt(3))): n in [1..80]]; // Vincenzo Librandi, Oct 25 2011
CROSSREFS
Sequence in context: A214989 A228177 A172329 * A313055 A313056 A313057
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 30 2010
EXTENSIONS
Typo in formula corrected by Vincenzo Librandi, Oct 25 2011
STATUS
approved