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A182778 Beatty sequence for 3 + sqrt(3). 3
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 (list; graph; refs; listen; history; text; internal format)
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

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Cf. A182760, A182777.

Sequence in context: A214989 A228177 A172329 * A313055 A313056 A313057

Adjacent sequences:  A182775 A182776 A182777 * A182779 A182780 A182781

KEYWORD

nonn

AUTHOR

Clark Kimberling, Nov 30 2010

EXTENSIONS

Typo in formula corrected by Vincenzo Librandi, Oct 25 2011

STATUS

approved

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Last modified October 17 21:32 EDT 2019. Contains 328133 sequences. (Running on oeis4.)