A081168 -id:A081168 - cp's OEIS frontend

A177102 Beatty sequence for sqrt(10).

3, 6, 9, 12, 15, 18, 22, 25, 28, 31, 34, 37, 41, 44, 47, 50, 53, 56, 60, 63, 66, 69, 72, 75, 79, 82, 85, 88, 91, 94, 98, 101, 104, 107, 110, 113, 117, 120, 123, 126, 129, 132, 135, 139, 142, 145, 148, 151, 154, 158, 161, 164, 167, 170, 173, 177, 180, 183

Offset: 1

Clark Kimberling, Aug 16 2011

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

Cf. A010467, A194113.

Partial sums of A081168.

[Floor(n*Sqrt(10)): n in [1..60]]; // Vincenzo Librandi, Oct 24 2011

Mathematica
```
Table[Floor[n*Sqrt[10]],{n,1,100}]
```

for(n=1,50, print1(floor(n*sqrt(10)), ", ")) \\ G. C. Greubel, Sep 24 2017

a(n) = floor(n*sqrt(10)).

A081129 Differences of Beatty sequence for cube root of 3.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2

Offset: 0

Benoit Cloitre, Apr 16 2003

nonn

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A059539, A081117, A081147, A081168.

A081129:= func< n | Floor((n+1)*3^(1/3)) - Floor(n*3^(1/3)) >;
[A081129(n): n in [0..120]]; // G. C. Greubel, Jan 15 2024

Differences[Floor[Range[0,110]Surd[3,3]]] (* Harvey P. Dale, Apr 06 2022 *)

a(n)=floor((n+1)*3^(1/3))-floor(n*3^(1/3))

def A081129(n): return floor((n+1)*3^(1/3)) - floor(n*3^(1/3))
[A081129(n) for n in range(121)] # G. C. Greubel, Jan 15 2024

a(n) = floor((n+1)*3^(1/3)) - floor(n*3^(1/3)).

A081147 First differences of A022839.

Original entry on oeis.org

2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2

Offset: 0

Benoit Cloitre, Apr 16 2003

nonn

Differences of Beatty sequence for square root of 5.

Let S(0) = 2; obtain S(k) from S(k-1) by applying 2 -> 2223, 3 -> 22223; sequence is S(0), S(1), S(2), ...

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A022839, A081168.

A081147:= func< n | Floor((n+1)*Sqrt(5)) - Floor(n*Sqrt(5)) >;
[A081147(n): n in [0..120]]; // G. C. Greubel, Jan 15 2024

Flatten[ Table[ Nest[ Flatten[ # /. {2 -> {2, 2, 2, 3}, 3 -> {2, 2, 2, 2, 3}}] &, {2}, n], {n,0,4}]] (* Robert G. Wilson v, May 07 2005 *)
Differences[Table[Floor[n Sqrt[5]],{n,0,110}]] (* Harvey P. Dale, May 05 2019 *)

a(n)=floor((n+1)*sqrt(5))-floor(n*sqrt(5))

def A081147(n): return floor((n+1)*sqrt(5)) - floor(n*sqrt(5))
[A081147(n) for n in range(121)] # G. C. Greubel, Jan 15 2024

a(n) = floor((n+1)*sqrt(5)) - floor(n*sqrt(5)).

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A177102 Beatty sequence for sqrt(10).

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A081129 Differences of Beatty sequence for cube root of 3.

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A081147 First differences of A022839.

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