A171982 -id:A171982 - cp's OEIS frontend

A246170 Beatty sequence for sqrt(14).

3, 7, 11, 14, 18, 22, 26, 29, 33, 37, 41, 44, 48, 52, 56, 59, 63, 67, 71, 74, 78, 82, 86, 89, 93, 97, 101, 104, 108, 112, 115, 119, 123, 127, 130, 134, 138, 142, 145, 149, 153, 157, 160, 164, 168, 172, 175, 179, 183, 187, 190, 194, 198, 202, 205, 209, 213

Offset: 1

Vincenzo Librandi, Aug 20 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. Beatty sequence for sqrt(k): A001951 (k=2), A022838 (k=3), A022839 (k=5), A022840 (k=6), A022841 (k=7), A022842 (k=8), A177102 (k=10), A171982 (k=11), A194028 (k=12), A173983 (k=13), this sequence (k=14), A246171 (k=15), A171984 (k=17).

Magma
```
[Floor(n*Sqrt(14)): n in [1..80]];
```

a[n_]:=Floor[n Sqrt[14]]; Array[a, 80, 1]

a(n) = floor(n*sqrt(14)).

A194114 Sum{floor(j*sqrt(11)) : 1<=j<=n}; n-th partial sum of Beatty sequence for sqrt(11).

Original entry on oeis.org

3, 9, 18, 31, 47, 66, 89, 115, 144, 177, 213, 252, 295, 341, 390, 443, 499, 558, 621, 687, 756, 828, 904, 983, 1065, 1151, 1240, 1332, 1428, 1527, 1629, 1735, 1844, 1956, 2072, 2191, 2313, 2439, 2568, 2700, 2835, 2974, 3116, 3261, 3410, 3562, 3717

Offset: 1

Clark Kimberling, Aug 16 2011

nonn

Cf. A171982 (Beatty sequence for sqrt(11)).

c[n_] := Sum[Floor[j*Sqrt[11]], {j, 1, n}];
c = Table[c[n], {n, 1, 90}]

A198266 a(n) = ceiling(n*sqrt(11)).

Original entry on oeis.org

0, 4, 7, 10, 14, 17, 20, 24, 27, 30, 34, 37, 40, 44, 47, 50, 54, 57, 60, 64, 67, 70, 73, 77, 80, 83, 87, 90, 93, 97, 100, 103, 107, 110, 113, 117, 120, 123, 127, 130, 133, 136, 140, 143, 146, 150, 153, 156, 160, 163, 166, 170, 173, 176, 180

Offset: 0

Vincenzo Librandi, Oct 24 2011

The first term where this sequence is different from A067497 is a(22)=73, compared with A067497(22)=74. - Jean-François Alcover, Jan 29 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A067497, A171982.

Magma
```
[Ceiling(n*Sqrt(11)): n in [0..60]]
```

Ceiling[Range[0,60]Sqrt[11]] (* Harvey P. Dale, Aug 20 2017 *)

A198267 Round(n*sqrt(11)).

Original entry on oeis.org

0, 3, 7, 10, 13, 17, 20, 23, 27, 30, 33, 36, 40, 43, 46, 50, 53, 56, 60, 63, 66, 70, 73, 76, 80, 83, 86, 90, 93, 96, 99, 103, 106, 109, 113, 116, 119, 123, 126, 129, 133, 136, 139, 143, 146, 149, 153, 156, 159, 163, 166, 169, 172, 176, 179

Offset: 0

Vincenzo Librandi, Oct 24 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A067497, A171982.

Magma
```
[Round(n*Sqrt(11)): n in [0..60]]
```

cp's OEIS Frontend

A246170 Beatty sequence for sqrt(14).

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A194114 Sum{floor(j*sqrt(11)) : 1<=j<=n}; n-th partial sum of Beatty sequence for sqrt(11).

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Mathematica

A198266 a(n) = ceiling(n*sqrt(11)).

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Magma

Mathematica

A198267 Round(n*sqrt(11)).

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Magma