A191381 -id:A191381 - cp's OEIS frontend

A191340 (A022839 mod 2)+(A108598 mod 2).

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

Offset: 1

Clark Kimberling, Jun 01 2011

nonn

Let r=sqrt(5) and s=r/(r-1).  There numbers yield the following two complementary Beatty sequences:
A022839(n)=[nr], A108598(n)=[ns], where [ ]=floor.
A191340(n)=the number of odd numbers in {[nr], [ns]}.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191329, A191336, A191380, A191381, A191382.

r = Sqrt[5]; s = r/(r - 1); h = 120;
u = Table[Floor[n*r], {n, 1, h}] (* A022839 *)
v = Table[Floor[n*s], {n, 1, h}] (* A108598 *)
w = Mod[u, 2] + Mod[v, 2] (* A191340 *)
Flatten[Position[w, 0]]  (* A191380 *)
Flatten[Position[w, 1]]  (* A191381 *)
Flatten[Position[w, 2]]  (* A191382 *)

a(n)=([nr] mod 2)+([ns] mod 2), where r=sqrt(5), s=r/(r-1), [ ]=floor.

A191380 Positions of 0 in A191340.

Original entry on oeis.org

9, 10, 17, 18, 19, 20, 27, 28, 29, 37, 38, 51, 52, 60, 61, 62, 69, 70, 71, 72, 79, 80, 94, 102, 103, 104, 111, 112, 113, 114, 121, 122, 131, 136, 145, 146, 153, 154, 155, 156, 163, 164, 165, 173, 178, 187, 188, 195, 196, 197, 198, 205, 206, 207, 215, 216, 229, 230, 238, 239, 240, 247, 248, 249, 257, 258, 272, 280, 281, 282, 289, 290

Offset: 1

Clark Kimberling, Jun 01 2011

nonn

See A191340.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191340.

Cf. A191381, A191382 (positions of 1 and 2 in the same).

Mathematica
```
(See A191340.)
```

A191382 Positions of 2 in A191340.

Original entry on oeis.org

5, 13, 14, 15, 22, 23, 24, 25, 32, 33, 42, 47, 56, 57, 64, 65, 66, 67, 74, 75, 76, 84, 89, 98, 99, 106, 107, 108, 109, 116, 117, 118, 126, 127, 140, 141, 149, 150, 151, 158, 159, 160, 168, 169, 183, 191, 192, 193, 200, 201, 202, 203, 210, 211, 220, 225, 233, 234, 235, 242, 243, 244, 245, 252, 253, 254, 262, 267, 276, 277, 284, 285

Offset: 1

Clark Kimberling, Jun 01 2011

nonn

See A191340.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191340.

Cf. A191380, A191381 (positions of 0 and 1 in the same).

Mathematica
```
(See A191340.)
```

cp's OEIS Frontend

A191340 (A022839 mod 2)+(A108598 mod 2).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A191380 Positions of 0 in A191340.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A191382 Positions of 2 in A191340.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica