A190492 -id:A190492 - cp's OEIS frontend

A190491 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),3,1) and []=floor.

1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 1, 3, 1, 2, 0, 2, 0, 1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 0, 1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 1, 3, 1, 2, 0, 2, 0, 1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 2, 0, 2, 0

Offset: 1

Clark Kimberling, May 11 2011

nonn

Write a(n)=[(bn+c)r]-b[nr]-[cr].  If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b.  The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b.  These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1):  A190427-A190430
(sqrt(2),2,0):  A190480, A120743, A170749
(sqrt(2),2,1):  A190483-A190486
(sqrt(2),3,0):  A190487-A190490
(sqrt(2),3,1):  A190491-A190495
(sqrt(2),3,2):  A190496-A190500

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A190492, A190493, A190494, A190495.

r = Sqrt[2]; b = 3; c = 1;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}]  (* A190491 *)
Flatten[Position[t, 0]]   (* A190492 *)
Flatten[Position[t, 1]]   (* A190493 *)
Flatten[Position[t, 2]]   (* A190494 *)
Flatten[Position[t, 3]]   (* A190495 *)

A190495 Positions of 3 in A190491.

Original entry on oeis.org

7, 12, 19, 24, 36, 41, 48, 53, 65, 70, 77, 82, 89, 94, 106, 111, 118, 123, 135, 140, 147, 152, 164, 176, 181, 188, 193, 205, 210, 217, 222, 234, 239, 246, 251, 258, 263, 275, 280, 287, 292, 304, 309, 316, 321, 328, 333, 345, 350, 357, 362, 374, 379, 386, 391, 403, 408, 415, 420

Offset: 1

Clark Kimberling, May 11 2011

nonn

See A190492.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A190491.

Mathematica
```
(See A190491.)
```

A190493 Positions of 1 in A190491.

Original entry on oeis.org

1, 3, 6, 8, 13, 15, 18, 20, 23, 25, 30, 32, 35, 37, 42, 44, 47, 49, 54, 56, 59, 61, 64, 66, 71, 73, 76, 78, 83, 85, 88, 90, 93, 95, 100, 102, 105, 107, 112, 114, 117, 119, 124, 129, 131, 134, 136, 141, 143, 146, 148, 153, 155, 158, 160, 163, 165, 170, 172, 175, 177, 182, 184, 187, 189, 194, 199, 201, 204, 206, 211, 213, 216, 218, 223

Offset: 1

Clark Kimberling, May 11 2011

nonn

(See A190492.)

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A190491.

Mathematica
```
(See A190492.)
```

cp's OEIS Frontend

A190491 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),3,1) and []=floor.

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A190495 Positions of 3 in A190491.

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A190493 Positions of 1 in A190491.

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