A072787 -id:A072787 - cp's OEIS frontend

A072789 The size of the parenthesizations obtained with the global ranking/unranking scheme presented in A072787-A072788.

1, 2, 2, 3, 3, 3, 4, 3, 4, 4, 4, 4, 3, 4, 5, 4, 5, 4, 4, 4, 5, 5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 4, 6, 5, 5, 6, 5, 5, 6, 5, 6, 6, 5, 5, 5, 6, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 5, 6, 5, 6, 6, 6, 7, 6, 6, 7, 5, 6, 7, 7, 6, 6, 6, 5, 6, 7, 6, 7, 7, 6, 6, 7, 7, 7, 6, 5, 5

Offset: 1

Antti Karttunen, Jun 12 2002

To get a cleaner looking table, the term a(0)=0 is not listed here.

A072790(n) gives the maximum position where the value n occurs. See the comment at A072787. Same triangle computed modulo 2: A072792.

A072788 Inverse permutation to A072787.

Original entry on oeis.org

0, 1, 3, 2, 8, 5, 4, 22, 7, 13, 10, 17, 18, 6, 9, 36, 21, 64, 19, 15, 12, 27, 46, 50, 16, 14, 41, 24, 31, 59, 58, 47, 60, 38, 37, 32, 11, 45, 20, 191, 44, 52, 120, 40, 23, 78, 63, 148, 144, 56, 43, 51, 111, 108, 35, 106, 61, 196, 168, 131, 178, 153, 150, 115, 116, 33, 29

Offset: 0

Antti Karttunen, Jun 12 2002

A. Karttunen, Gatomorphisms
Index entries for sequences that are permutations of the natural numbers

Inverse permutation: A072787. Cf. also A072740, A072741, A072789.

A072734 Simple triangle-stretching N X N -> N bijection, variant of A072732.

Original entry on oeis.org

0, 1, 2, 3, 12, 4, 7, 17, 18, 5, 6, 23, 40, 24, 8, 11, 31, 49, 50, 25, 9, 10, 30, 59, 84, 60, 32, 13, 16, 39, 71, 97, 98, 61, 33, 14, 15, 38, 70, 111, 144, 112, 72, 41, 19, 22, 48, 83, 127, 161, 162, 113, 73, 42, 20, 21, 47, 82, 126, 179, 220, 180, 128, 85, 51, 26, 29, 58

Offset: 0

Antti Karttunen, Jun 12 2002

Index entries for sequences that are permutations of the natural numbers

Inverse: A072735, projections: A072740 & A072741, variant of the same theme: A072732. Used to construct the global arithmetic ranking scheme of plane binary trees presented in A072787/A072788. Cf. also A001477 and its projections A025581 & A002262.

(define (A072734 n) (packA072734 (A025581 n) (A002262 n)))
(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
(define (packA072734 x y) (let ((x-y (- x y))) (cond ((negative? x-y) (packA001477 (+ (* 2 x) (modulo (1+ x-y) 2)) (+ (* 2 x) (floor->exact (/ (+ (- x-y) (modulo x-y 2)) 2))))) ((< x-y 3) (packA001477 (+ (* 2 y) x-y) (* 2 y))) (else (packA001477 (+ (* 2 y) (floor->exact (/ (1+ x-y) 2)) (modulo (1+ x-y) 2)) (+ (* 2 y) (modulo x-y 2)))))))

A072790 Maximum position in A072789 where the value n occurs.

Original entry on oeis.org

0, 1, 3, 13, 38, 230, 6902, 5963330, 4445170540277, 2469942641522759680444872, 762577081551553466590743598512392989564579443140, 72690475663460578305076472056787461439583062421562715705151023011944336192599271053989785936377

Offset: 0

Antti Karttunen, Jun 12 2002

nonn

Binary widths given by A072791. See the comment at A072787.

A072791 Binary widths of A072790.

Original entry on oeis.org

0, 1, 2, 4, 6, 8, 13, 23, 43, 82, 160, 316, 628, 1252, 2500, 4997

Offset: 0

Antti Karttunen, Jun 12 2002

See the comment at A072787. Compare for example with A072641 and A072642.

a(12)-a(15) from Sean A. Irvine, Oct 27 2024

cp's OEIS Frontend

A072789 The size of the parenthesizations obtained with the global ranking/unranking scheme presented in A072787-A072788.

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A072788 Inverse permutation to A072787.

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A072734 Simple triangle-stretching N X N -> N bijection, variant of A072732.

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A072790 Maximum position in A072789 where the value n occurs.

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A072791 Binary widths of A072790.

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