A074683 Permutation of natural numbers induced by the Catalan Automorphism *A074683 acting on parenthesizations as encoded and ordered by A014486/A063171.

0, 1, 3, 2, 7, 6, 8, 5, 4, 17, 16, 18, 15, 14, 20, 19, 22, 12, 11, 21, 13, 10, 9, 45, 44, 46, 43, 42, 48, 47, 50, 40, 39, 49, 41, 38, 37, 54, 53, 55, 52, 51, 61, 60, 63, 31, 30, 62, 32, 29, 28, 57, 56, 64, 34, 33, 59, 36, 26, 25, 58, 35, 27, 24, 23, 129, 128, 130, 127, 126

Offset: 0

Author

Antti Karttunen, Sep 11 2002

Keywords

• nonn

Comments

This bijection maps between the "standard" ordering of binary trees as encoded by A014486 and "variant A quaternary encoding" as explained in the sequence A085184.

This is a rare example of Catalan Automorphism (with simple definition) where the cycle count sequence (A089411) is not monotone. (See A127296 for more complex example.)

Links

• A. Karttunen, Catalan Automorphisms
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Row 12 of A122202. Inverse of A074684. a(n) = A057163(A074682(A057163(n))).

The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in subpermutations limited by A014137 and A014138 are given by A089411, A086586 and A089412.