A071663 -id:A071663 - cp's OEIS frontend

A083929 Inverse function of N -> N injection A083930.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Antti Karttunen, May 13 2003

nonn

a(0)=0 because A083930(0)=0, but a(n) = 0 also for those n which do not occur as values of A083930. All positive natural numbers occur here once.

It appears that A071661(n) = A083929(A071663(A083930(n))) and A071662 = A083929(A071664(A083930(n))).

a(A080930(n)) = n for all n. Cf. A083925-A083928, A083935.

a(n) = A083927(A083925(n)).

A125979 Signature-permutation of a Catalan automorphism: composition of A125976 and A057164.

Original entry on oeis.org

0, 1, 3, 2, 8, 5, 6, 7, 4, 22, 13, 15, 18, 10, 19, 11, 20, 21, 12, 14, 16, 17, 9, 64, 36, 41, 50, 27, 52, 29, 55, 59, 32, 38, 43, 46, 24, 60, 33, 39, 47, 25, 61, 34, 62, 63, 35, 40, 48, 49, 26, 51, 28, 53, 56, 30, 54, 57, 58, 31, 37, 42, 44, 45, 23, 196, 106, 120, 148, 78

Offset: 0

Antti Karttunen, Jan 02 2007

nonn

This is self-inverse permutation (involution) of the nonnegative integers.

Index entries for signature-permutations of Catalan automorphisms

a(n) = A125976(A057164(n)) = A057164(A125976(n)). Differs from A071663 for the first time at n=43, where a(n)=34, while A071663(n)=48.

cp's OEIS Frontend

A083929 Inverse function of N -> N injection A083930.

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