A083927 -id:A083927 - cp's OEIS frontend

A130920 Signature permutation of a Catalan automorphism: DEEPEN-transform of automorphism *A057512.

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 14, 10, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 37, 24, 42, 51, 25, 38, 26, 44, 47, 27, 53, 56, 60, 28, 39, 29, 43, 52, 30, 40, 31, 45, 48, 32, 54, 49, 50, 33, 41, 34, 46, 55, 35, 57, 58, 62, 36, 61, 59, 63, 64, 65, 107, 66, 121, 149, 67

Offset: 0

Antti Karttunen, Jun 11 2007

nonn

*A130920 = DEEPEN(*A057512) = NEPEED(*A057512) = DEEPEN(DEEPEN(*A057510)) = NEPEED(NEPEED(*A057510)). See A122283, A122284 for the definitions of DEEPEN and NEPEED transforms.

Inverse: A130919. A122351(n) = A083927(A130920(A057123(n))).

A083926 Inverse function of N -> N injection A072795.

Original entry on oeis.org

0, 0, 1, 0, 2, 3, 0, 0, 0, 4, 5, 6, 7, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 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, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44

Offset: 0

Antti Karttunen, May 13 2003

nonn

a(1)=0 because A072795(0)=1, but a(n) = 0 also for those n which do not occur as values of A072795. All positive natural numbers occur here once.

a(A072795(n)) = n for all n. Cf. A083925, A083927-A083929, A083935.

a(n) = A083924(n)*A072772(n).

A122300 Row 2 of A122283 and A122284. An involution of nonnegative integers.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 14, 16, 19, 11, 15, 12, 17, 20, 13, 18, 21, 22, 23, 24, 25, 26, 27, 37, 38, 42, 44, 53, 51, 47, 56, 60, 28, 29, 39, 43, 52, 30, 40, 31, 45, 46, 34, 54, 57, 61, 33, 41, 32, 48, 55, 35, 49, 58, 62, 36, 50, 59, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 0

Antti Karttunen, Sep 01 2006

nonn

The signature-permutation of the automorphism which is derived from the second non-recursive automorphism *A072796 either with recursion schema DEEPEN or NEPEED. (see A122283, A122284 for their definitions).

Index entries for signature-permutations of Catalan automorphisms

A057163(n) = A083927(A122300(A057123(n))).

A122313 Row 8 of A122283.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 17, 18, 16, 14, 15, 21, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 34, 36, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 58, 59, 56, 51, 52, 57, 53, 54, 55, 63, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 0

Antti Karttunen, Sep 01 2006

nonn

The signature-permutation of the automorphism which is derived from the eighth non-recursive automorphism *A072797 with recursion schema DEEPEN (see A122283 for the definition).

Index entries for signature-permutations of Catalan automorphisms

Inverse: A122314. A082325(n) = A083927(A122313(A057123(n))). Differs from A069775 for the first time at n=34, where a(n)=35, while A069775(n)=34.

A122314 Row 8 of A122284.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 17, 18, 16, 14, 15, 20, 21, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 34, 36, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 54, 55, 57, 58, 59, 53, 56, 51, 52, 61, 62, 63, 60, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 0

Antti Karttunen, Sep 01 2006

nonn

The signature-permutation of the automorphism which is derived from the eighth non-recursive automorphism *A072797 with recursion schema NEPEED (see A122284 for the definition).

Index entries for signature-permutations of Catalan automorphisms

Inverse: A122313. A082326(n) = A083927(A122314(A057123(n))). Differs from A069776 for the first time at n=34, where a(n)=35, while A069776(n)=34.

A123502 Signature permutation of a Catalan automorphism: first recurse into the left subtree of the right hand side subtree of a binary tree and after that apply *A123498 at the root.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 10, 17, 16, 18, 11, 20, 12, 14, 15, 13, 19, 21, 22, 23, 24, 25, 26, 27, 45, 46, 44, 42, 49, 48, 43, 47, 50, 28, 29, 54, 53, 55, 30, 57, 31, 37, 38, 32, 39, 40, 41, 33, 61, 34, 51, 52, 35, 56, 58, 59, 36, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 0

Antti Karttunen, Oct 11 2006

nonn

Index entries for signature-permutations of Catalan automorphisms

Inverse: A123501. A057502(n) = A083927(a(A057123(n))) = A083927(A085160(A057123(n))).

cp's OEIS Frontend

A130920 Signature permutation of a Catalan automorphism: DEEPEN-transform of automorphism *A057512.

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A083926 Inverse function of N -> N injection A072795.

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Formula

A122300 Row 2 of A122283 and A122284. An involution of nonnegative integers.

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A122313 Row 8 of A122283.

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A122314 Row 8 of A122284.

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A123502 Signature permutation of a Catalan automorphism: first recurse into the left subtree of the right hand side subtree of a binary tree and after that apply *A123498 at the root.

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