A182777 -id:A182777 - cp's OEIS frontend

A182778 Beatty sequence for 3 + sqrt(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

Offset: 1

Clark Kimberling, Nov 30 2010

nonn

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.

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

Cf. A182760, A182777.

[Floor(n*(3+Sqrt(3))): n in [1..80]]; // Vincenzo Librandi, Oct 25 2011

Mathematica
```
Table[Floor[(3+Sqrt[3])*n], {n, 54}]
```

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)

Typo in formula corrected by Vincenzo Librandi, Oct 25 2011

A194142 a(n) = Sum_{j=1..n} floor(j*(3-sqrt(3))); n-th partial sum of Beatty sequence for 3-sqrt(3).

Original entry on oeis.org

1, 3, 6, 11, 17, 24, 32, 42, 53, 65, 78, 93, 109, 126, 145, 165, 186, 208, 232, 257, 283, 310, 339, 369, 400, 432, 466, 501, 537, 575, 614, 654, 695, 738, 782, 827, 873, 921, 970, 1020, 1071, 1124, 1178, 1233, 1290, 1348, 1407, 1467, 1529, 1592, 1656

Offset: 1

Clark Kimberling, Aug 17 2011

nonn

Partial sums of A182777.

c[n_] := Sum[Floor[j*(3-Sqrt[3])], {j, 1, n}];
c = Table[c[n], {n, 1, 90}]

cp's OEIS Frontend

A182778 Beatty sequence for 3 + sqrt(3).

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