cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A072660 Size of the parenthesizations obtained with the global ranking/unranking scheme A072656-A072659.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 5, 4, 4, 4, 5, 4, 4, 6, 5, 5, 5, 5, 4, 6, 5, 4, 4, 5, 7, 6, 6, 6, 5, 5, 5, 6, 5, 5, 7, 6, 6, 6, 5, 4, 6, 5, 8, 7, 7, 7, 6, 7, 6, 6, 6, 6, 5, 7, 6, 5, 4, 6, 8, 7, 7, 7, 6, 6, 5, 7, 5, 5, 8, 6, 6, 9, 8, 8, 8, 7, 8, 7, 7, 9, 7, 7, 7, 6, 6, 5, 7, 5, 6, 8, 7, 7, 6, 6, 4, 7, 5, 9, 8
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Crossrefs

Cf. A072657-A072659. Permutations: A071673, A072643, A072644, A072645.

A072657 Inverse permutation to A072656.

Original entry on oeis.org

0, 1, 3, 2, 8, 6, 5, 7, 19, 22, 15, 4, 52, 16, 13, 20, 60, 18, 14, 178, 43, 51, 61, 41, 11, 153, 53, 10, 21, 47, 555, 155, 177, 136, 42, 33, 64, 179, 55, 39, 557, 125, 151, 181, 38, 12, 150, 56, 1799, 479, 553, 417, 154, 552, 164, 135, 192, 117, 36, 471, 191, 29, 17
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

A072657(n) = A057163(A072659(n)). A072660 gives the size of the corresponding parenthesizations, i.e. A072660(n) = A029837(A014486(A072657(n))+1)/2 [A029837(n+1) gives the binary width of n].

A072634 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using A054238 as the pairing function N X N -> N.

Original entry on oeis.org

0, 1, 3, 2, 11, 9, 4, 6, 5, 139, 131, 33, 41, 35, 12, 10, 8, 70, 66, 7, 17, 21, 18, 32907, 32779, 2051, 2179, 2059, 161, 137, 129, 8233, 8201, 43, 515, 547, 521, 140, 132, 34, 42, 36, 16, 14, 72, 16454, 16390, 68, 1026, 1090, 1030, 15, 13, 19, 81, 69, 23, 65
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

Inverse permutation: A072635.
Cf. A014486, A000695, A054238, A071651, A072636, A072646, A072656, A072658, A072644.
Cf. also A296689.

Programs

  • Scheme
    ;; Functions below show the essential idea:
(define A072634 (lexrank->arithrank-bijection packA054238))
(define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))
(define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
(define (packA054238 x y) (+ (A000695 x) (* 2 (A000695 y))))

A072636 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA054238tr as the packing bijection N X N -> N.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 4, 9, 11, 18, 21, 17, 66, 70, 7, 8, 10, 35, 41, 12, 33, 131, 139, 261, 274, 258, 4101, 4117, 22, 65, 69, 1030, 1090, 81, 1026, 16390, 16454, 20, 23, 19, 68, 72, 13, 14, 36, 521, 547, 42, 515, 8201, 8233, 15, 16, 34, 43, 129, 132, 137, 2059, 2179
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

Inverse permutation: A072637. Cf. also A014486, A000695, A054238, A071651, A072634, A072646, A072656, A072658, A072644.

A072787 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using A072734 as the packing bijection N X N -> N.

Original entry on oeis.org

0, 1, 3, 2, 6, 5, 13, 8, 4, 14, 10, 36, 20, 9, 25, 19, 24, 11, 12, 18, 38, 16, 7, 44, 27, 209, 77, 21, 105, 66, 104, 28, 35, 65, 230, 54, 15, 34, 33, 75, 43, 26, 85, 50, 40, 37, 22, 31, 191, 67, 23, 51, 41, 69, 107, 68, 49, 92, 30, 29, 32, 56, 211, 46, 17, 299, 120, 5671
Offset: 0

Views

Author

Antti Karttunen, Jun 12 2002

Keywords

Comments

This ranking scheme condenses the structures of the same size (cf. A072789) somewhat better than scheme presented in A072656 (which uses the N X N -> N bijection A072793). Compare the sequences A072790 and A072640 giving the max positions where the last structure with size n will occur in these orderings and the respective binary widths A072791 & A072642. However, by using the second or third power of the bijection A072734 one gets even better results in a certain range.

Links

Crossrefs

Inverse permutation: A072788. Cf. also A014486, A072734, A072789.

A072658 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA048680oA054238tr as the packing bijection N X N -> N.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 11, 9, 28, 15, 17, 62, 8, 13, 10, 14, 45, 18, 24, 27, 100, 36, 187, 117, 91, 1292, 22, 70, 38, 72, 680, 93, 111, 295, 1229, 16, 47, 26, 29, 102, 12, 20, 23, 58, 302, 73, 189, 147, 2090, 21, 34, 39, 35, 113, 44, 61, 116, 1100, 162, 150, 179, 477
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

Inverse permutation: A072659. Cf. also A014486, A000695, A054238, A048680, A071651, A072634, A072636, A072646, A072656, A072660.

A072793 Simple tabular N X N -> N bijection: first interleave the bits as with A054238, then apply the bijection A048680.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 8, 12, 11, 17, 13, 14, 15, 19, 20, 22, 23, 16, 25, 18, 33, 24, 38, 26, 27, 28, 30, 31, 40, 41, 43, 44, 21, 46, 32, 51, 29, 67, 45, 72, 34, 35, 36, 53, 54, 48, 49, 74, 75, 56, 57, 37, 59, 39, 88, 50, 80, 52, 122, 58, 93, 60, 61, 62, 64, 65, 82, 83
Offset: 0

Views

Author

Antti Karttunen, Jun 12 2002

Keywords

Links

Crossrefs

Inverse: A072794. Composition of A048680 & A054238. The X-projection: A072661, The Y-projection: A072662. Used in global arithmetic ranking scheme presented in A072656.
Showing 1-7 of 7 results.

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