A065251 -id:A065251 - cp's OEIS frontend

A065252 The sequence A065251 reduced modulo 3 (i.e., replace every -1 with 2).

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

Offset: 1

Antti Karttunen, Oct 25 2001

nonn

Maple
```
[seq((A065251(j) mod 3),j=1..120)];
```

a(0)=0, a(2n) = 2 - a(n), a(2n+1) = 2 - ((a(n)+1) mod 3).

A120705 Permutation of natural numbers induced by the Catalan bijection gma120705 acting on the binary trees encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 4, 5, 6, 22, 21, 17, 18, 20, 10, 9, 11, 13, 12, 14, 15, 19, 16, 64, 63, 58, 59, 62, 46, 45, 48, 50, 49, 54, 55, 61, 57, 27, 26, 23, 24, 25, 29, 28, 33, 34, 35, 30, 36, 32, 31, 38, 37, 39, 41, 40, 51, 52, 60, 56, 42, 43, 44, 47, 53, 196, 195, 189, 190, 194

Offset: 0

Antti Karttunen, Jun 28 2006

nonn

When the automorphisms A120705/A120705 act on the full Stern-Brocot tree (A007305/A047679), which is an infinite binary tree, they will move each fraction r to the position of 2*r (or r/2 respectively). See comments at A065249 and A065251. (Proof in preparation, to be published.)

A. Karttunen, Gatomorphisms (With the complete Scheme source)
N. J. A. Sloane, Stern-Brocot or Farey Tree
Index entries for signature-permutations induced by Catalan automorphisms

Inverse of A120706. Cf. A074680.

Number of cycles: A120707. Number of fixed-points: A019590. Max. cycle size: A120708. LCM of cycle sizes: A120709.

A065249 Permutation of N induced by the order-preserving permutation of the positive rational numbers (x -> x/2), positions in Stern-Brocot tree.

Original entry on oeis.org

2, 8, 1, 32, 4, 11, 6, 128, 16, 35, 18, 5, 47, 24, 3, 512, 64, 131, 66, 17, 143, 72, 9, 21, 44, 23, 191, 96, 12, 27, 14, 2048, 256, 515, 258, 65, 527, 264, 33, 69, 140, 71, 575, 288, 36, 75, 38, 10, 87, 176, 22, 93, 188, 95, 767, 384, 48, 99, 50, 13, 111, 56, 7, 8192

Offset: 1

Antti Karttunen, Oct 25 2001

nonn

Cf. A057114, A065251. Inverse permutation: A065250.

[seq(A065249(j),j=1..120)]; A065249 := n -> frac2position_in_whole_SB_tree((SternBrocotTreeNum(n)/SternBrocotTreeDen(n))/2);

A065250 Permutation of N induced by the order-preserving permutation of the positive rational numbers (x -> 2x), positions in Stern-Brocot tree.

Original entry on oeis.org

3, 1, 15, 5, 12, 7, 63, 2, 23, 48, 6, 29, 60, 31, 255, 9, 20, 11, 95, 192, 24, 51, 26, 14, 119, 240, 30, 125, 252, 127, 1023, 4, 39, 80, 10, 45, 92, 47, 383, 768, 96, 195, 98, 25, 207, 104, 13, 57, 116, 59, 479, 960, 120, 243, 122, 62, 503, 1008, 126, 509, 1020, 511

Offset: 1

Antti Karttunen, Oct 25 2001

nonn

Cf. A057114, A065251. Inverse permutation A065249.

[seq(A065250(j),j=1..120)]; A065250 := n -> frac2position_in_whole_SB_tree((SternBrocotTreeNum(n)/SternBrocotTreeDen(n))*2);

cp's OEIS Frontend

A065252 The sequence A065251 reduced modulo 3 (i.e., replace every -1 with 2).

Views

Author

Keywords

Programs

Maple

Formula

A120705 Permutation of natural numbers induced by the Catalan bijection gma120705 acting on the binary trees encoded by A014486/A063171.

Views

Author

Keywords

Comments

Links

Crossrefs

A065249 Permutation of N induced by the order-preserving permutation of the positive rational numbers (x -> x/2), positions in Stern-Brocot tree.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

A065250 Permutation of N induced by the order-preserving permutation of the positive rational numbers (x -> 2x), positions in Stern-Brocot tree.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple