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A082313 Involution of natural numbers: A057501-conjugate of A057164. 6
0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 21, 14, 18, 13, 11, 22, 16, 17, 12, 19, 20, 10, 15, 23, 58, 37, 49, 35, 28, 62, 42, 46, 32, 51, 55, 27, 41, 25, 59, 39, 50, 36, 30, 63, 44, 45, 31, 53, 54, 26, 40, 33, 64, 47, 48, 34, 56, 57, 24, 38, 60, 61, 29, 43, 52, 65, 170, 107, 142, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Note: This is isomorphic with Meeussen's "skewcatacycleft" operation acting on the interpretation (gg) of the exercise 19 by Stanley.

LINKS

Table of n, a(n) for n=0..69.

Index entries for signature-permutations induced by Catalan automorphisms

R. P. Stanley, Exercises on Catalan and Related Numbers

FORMULA

a(n) = A057501(A057164(A057502(n)))

CROSSREFS

a(n) = A069888(A057502(n)). Occurs in A073200 as row 604463486276865131809167. Cf. also A082314, A082315, A082333, A082334.

Number of cycles: A007123. Number of fixed-points: A001405. Max. cycle size: A046698. LCM of cycle sizes: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Sequence in context: A123492 A123493 A123715 * A123494 A123716 A229927

Adjacent sequences:  A082310 A082311 A082312 * A082314 A082315 A082316

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 17 2003. Proposed by Wouter Meeussen in Dec 15 2001.

STATUS

approved

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Last modified August 26 03:27 EDT 2019. Contains 326324 sequences. (Running on oeis4.)