A269866 -id:A269866 - cp's OEIS frontend

A269865 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 11, 18, 27, 16, 25, 14, 21, 20, 13, 30, 45, 24, 17, 22, 33, 36, 23, 54, 81, 32, 19, 50, 75, 28, 35, 42, 63, 40, 55, 26, 39, 60, 37, 90, 135, 48, 49, 34, 51, 44, 29, 66, 99, 72, 41, 46, 69, 108, 91, 162, 243, 64, 85, 38, 57, 100, 125, 150, 225, 56, 31, 70, 105, 84, 47, 126, 189, 80, 43, 110, 165, 52

Offset: 1

Antti Karttunen, Mar 12 2016

This sequence can be represented as a binary tree. When the parent contains n, the left hand child contains 2n, while the value of right hand child is obtained by applying A250469(1+n):
                                    1
                                    |
                 ................../ \..................
                2                                       3
      4......../ \........5                   6......../ \........9
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  8       7          10       15         12       11         18       27
16 25   14 21      20  13   30  45     24  17   22  33     36  23   54  81
etc.
Note how all nodes with odd n have a right hand child with value 3n.

Antti Karttunen, Table of n, a(n) for n = 1..6142
Antti Karttunen, Entanglement Permutations, 2016-2017
Index entries for sequences that are permutations of the natural numbers

Inverse: A269866.
Cf. A250469.
Related or similar permutations: A269359, A269863, A269864, A269867, A246375, A249814, A252755, A270195.

a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

A269867 Self-inverse permutation of natural numbers: a(1) = 1, for even n, a(n) = A250469(1+a(n/2)), for odd n, a(n) = 2*a(A268674(n)-1).

Original entry on oeis.org

1, 3, 2, 9, 6, 5, 18, 27, 4, 11, 10, 15, 22, 23, 12, 81, 30, 7, 162, 33, 36, 13, 14, 45, 54, 29, 8, 69, 26, 17, 138, 243, 20, 37, 46, 21, 34, 167, 44, 99, 42, 41, 198, 39, 24, 35, 82, 135, 90, 91, 60, 87, 70, 25, 66, 207, 324, 65, 174, 51, 130, 149, 72, 729, 58, 55, 102, 111, 28, 53, 110, 63, 106, 77, 108, 501, 74, 115, 126, 297, 16, 47

Offset: 1

Antti Karttunen, Mar 12 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..3165
Index entries for sequences that are permutations of the natural numbers

Cf. A250469, A268674.

Similar permutations: A269865, A269866, A270197.

a(1) = 1, a(2n) = A250469(1+a(n)), a(2n+1) = 2*a(A268674(2n+1)-1).

A269864 Permutation of natural numbers: a(1) = 1, a(2n) = A269360(a(n)), a(2n+1) = A250469(1+a(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 10, 7, 8, 15, 16, 11, 26, 27, 28, 13, 12, 21, 22, 25, 36, 45, 46, 19, 14, 33, 76, 65, 66, 81, 82, 31, 18, 39, 34, 17, 56, 63, 64, 29, 50, 75, 106, 41, 116, 135, 136, 53, 24, 57, 40, 35, 86, 99, 226, 143, 120, 195, 196, 71, 206, 243, 244, 89, 38, 93, 52, 23, 96, 117, 100, 77, 20, 51, 166, 145, 156, 189, 190, 119, 32, 87

Offset: 1

Antti Karttunen, Mar 13 2016

This sequence can be represented as a binary tree. When the parent contains n, the left hand child contains A269360(n) [= 1+A250469(n)] and the right hand child contains A250469(1+n):
                                     1
                                     |
                  ................../ \..................
                 2                                       3
       4......../ \........5                   6......../ \........9
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  10       7           8       15         16       11         26       27
28  13   12 21       22 25   36  45     46  19   14  33     76  65   66  81
etc.

Antti Karttunen, Table of n, a(n) for n = 1..5887
Index entries for sequences that are permutations of the natural numbers

Inverse: A269863.
Cf. A250469, A269360.
Cf. also A269865, A269866, A269867.
Differs from similarly constructed A245606 for the first time at n=15, where a(15)=27 instead of 21.

a(1) = 1, a(2n) = 1 + A250469(a(n)), a(2n+1) = A250469(1+a(n)).

A270196 Permutation of natural numbers: a(1) = 1, a(2n) = 2a(n), a(A269369(1+n)) = 1 + 2a(n).

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 5, 8, 13, 14, 15, 12, 17, 10, 25, 16, 11, 26, 9, 28, 21, 30, 27, 24, 57, 34, 53, 20, 31, 50, 49, 32, 101, 22, 35, 52, 65, 18, 29, 56, 51, 42, 105, 60, 69, 54, 23, 48, 85, 114, 97, 68, 19, 106, 121, 40, 37, 62, 43, 100, 33, 98, 229, 64, 55, 202, 197, 44, 405, 70, 115, 104, 89, 130, 209, 36, 107, 58, 261, 112, 61

Offset: 1

Antti Karttunen, Mar 13 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8191
Index entries for sequences that are permutations of the natural numbers

Inverse: A270195.
Cf. A269369, A269370.
Related or similar permutations: A269866, A269373, A269376, A270197.

a(1) = 1, after which for even n, a(n) = 2*a(n/2), for odd n, a(n) = 1 + 2*a(A269370(n)-1).

A269359 Self-inverse permutation of natural numbers: a(1)=1, a(A269360(n)) = A250469(1+a(n)), a(A250469(1+n)) = A269360(a(n)).

Original entry on oeis.org

1, 3, 2, 9, 6, 5, 26, 11, 4, 27, 8, 65, 66, 25, 16, 15, 120, 71, 36, 169, 76, 33, 74, 41, 14, 7, 10, 81, 86, 185, 206, 215, 22, 195, 50, 19, 330, 515, 196, 75, 24, 337, 186, 49, 46, 45, 348, 247, 44, 35, 358, 213, 116, 353, 290, 143, 106, 507, 536, 295, 1266, 1345, 226, 99, 12, 13, 512, 2321, 220, 123, 18, 1285, 306, 23, 40, 21

Offset: 1

Antti Karttunen, Mar 13 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..607
Index entries for sequences that are permutations of the natural numbers

Cf. A250469, A268674, A269360.

Similar or related permutations: A244319, A269863, A269864, A269865, A269866, A269867.

a(1) = 1, after which for even n, a(n) = A250469(1+a(A268674(n-1))), for odd n, a(n) = A269360(a(A268674(n)-1)).
The declarative form can be expressed in terms of A250469 only:
a(1)=1, a(1+A250469(n)) = A250469(1+a(n)), a(A250469(1+n)) = 1+A250469(a(n)).

cp's OEIS Frontend

A269865 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

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A269867 Self-inverse permutation of natural numbers: a(1) = 1, for even n, a(n) = A250469(1+a(n/2)), for odd n, a(n) = 2*a(A268674(n)-1).

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Formula

A269864 Permutation of natural numbers: a(1) = 1, a(2n) = A269360(a(n)), a(2n+1) = A250469(1+a(n)).

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Formula

A270196 Permutation of natural numbers: a(1) = 1, a(2n) = 2a(n), a(A269369(1+n)) = 1 + 2a(n).

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Formula

A269359 Self-inverse permutation of natural numbers: a(1)=1, a(A269360(n)) = A250469(1+a(n)), a(A250469(1+n)) = A269360(a(n)).

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cp's OEIS Frontend

A269865 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(1+a(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A269867 Self-inverse permutation of natural numbers: a(1) = 1, for even n, a(n) = A250469(1+a(n/2)), for odd n, a(n) = 2*a(A268674(n)-1).

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Crossrefs

Formula

A269864 Permutation of natural numbers: a(1) = 1, a(2n) = A269360(a(n)), a(2n+1) = A250469(1+a(n)).

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Author

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Crossrefs

Formula

A270196 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(A269369(1+n)) = 1 + 2*a(n).

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Formula

A269359 Self-inverse permutation of natural numbers: a(1)=1, a(A269360(n)) = A250469(1+a(n)), a(A250469(1+n)) = A269360(a(n)).

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Formula

A270196 Permutation of natural numbers: a(1) = 1, a(2n) = 2a(n), a(A269369(1+n)) = 1 + 2a(n).