A273665 -id:A273665 - cp's OEIS frontend

A273667 Permutation of nonnegative integers: a(0) = 0, a(A153880(n)) = A255411(a(n)), a(A273670(n)) = A256450(a(n)).

0, 1, 4, 2, 6, 3, 18, 8, 12, 5, 24, 10, 48, 15, 16, 7, 30, 13, 56, 20, 21, 9, 36, 17, 96, 67, 60, 26, 27, 11, 72, 42, 22, 23, 120, 81, 240, 73, 66, 32, 33, 14, 87, 49, 28, 29, 144, 101, 360, 270, 88, 89, 80, 38, 90, 39, 52, 19, 107, 57, 288, 34, 76, 35, 168, 125, 416, 303, 109, 110, 99, 44, 420, 111, 108, 45, 61, 25, 112, 131, 64, 68, 327, 40

Offset: 0

Antti Karttunen, May 30 2016

Antti Karttunen, Table of n, a(n) for n = 0..5039
Indranil Ghosh, Python program for computing this sequence
Index entries for sequences related to factorial base representation
Index entries for sequences that are permutations of the natural numbers

Inverse: A273668.
Cf. A153880, A225901, A255411, A256450, A257680, A266193, A273663, A273670.
Similar or related permutations: A255566, A273665.

a(0) = 0; for n >= 1: if A257680(A225901(n)) = 0 [when n is one of the terms of A153880] then a(n) = A255411(a(A266193(n))), otherwise [when n is one of the terms of A273670], a(n) = A256450(a(A273663(n))).
As a composition of other permutations:
a(n) = A255566(A273665(n)).

A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2a(h).

Original entry on oeis.org

0, 1, 3, 7, 2, 15, 5, 31, 11, 63, 23, 127, 6, 47, 255, 13, 14, 95, 4, 511, 27, 29, 30, 191, 9, 1023, 55, 59, 61, 383, 19, 2047, 111, 119, 123, 767, 39, 4095, 223, 239, 247, 1535, 79, 8191, 447, 479, 495, 3071, 10, 159, 16383, 895, 62, 959, 991, 6143, 21, 319, 32767, 1791, 22, 125, 1919, 1983, 126, 12287, 46, 43, 639, 65535, 254, 3583, 12

Offset: 0

Antti Karttunen, May 05 2015

Because all terms of A255411 are even it means that even terms can only occur in even positions (together with some odd terms, for each one of which there is a separate infinite cycle), while terms in odd positions are all odd.

Inverse: A255566.
Cf. A000079, A000142, A001511, A001563, A083318, A255411, A256450, A257679, A257680, A257682, A257685.
Cf. also arrays A257503, A257505.
Related or similar permutations: A273665, A273668.

a(0) = 0; for n >= 1: if A257680(n) = 0 [i.e., n is one of the terms of A255411], then a(n) = 2*a(A257685(n)), otherwise [when n is one of the terms of A256450], a(n) = 1 + 2*a(A273662(n)).
Other identities:
For all n >= 1, A001511(a(n)) = A257679(n).
For all n >= 1, a(A001563(n)) = A000079(n-1) = 2^(n-1).
For all n >= 1, a(A000142(n)) = A083318(n-1).

Formula changed because of the changed starting offset of A256450 - Antti Karttunen, May 30 2016

A273666 Permutation of nonnegative integers: a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

Original entry on oeis.org

0, 1, 2, 3, 6, 4, 8, 5, 24, 10, 12, 7, 30, 13, 14, 9, 120, 34, 36, 16, 48, 18, 26, 11, 144, 42, 50, 19, 54, 20, 32, 15, 720, 154, 156, 46, 168, 49, 60, 22, 240, 66, 72, 25, 126, 37, 38, 17, 840, 186, 192, 58, 246, 68, 74, 27, 264, 73, 78, 28, 150, 44, 56, 21, 5040, 874, 876, 199, 888, 202, 204, 64, 960, 216, 242, 67, 288, 82, 84, 31

Offset: 0

Antti Karttunen, May 30 2016

This sequence can be represented as a binary tree. Each left hand child is produced as A153880(n), and each right hand child as A273670(n), when their parent contains n >= 1:
                                      0
                                      |
                   ...................1...................
                  2                                       3
        6......../ \........4                   8......../ \........5
       / \                 / \                 / \                 / \
      /   \               /   \               /   \               /   \
     /     \             /     \             /     \             /     \
   24       10         12       7          30       13         14       9
120  34   36  16     48  18   26 11     144  42   50  19     54  20   32 15
etc.

Inverse: A273665.
Cf. A153880, A273670.
Related or similar permutations: A255566, A273668.

a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

cp's OEIS Frontend

A273667 Permutation of nonnegative integers: a(0) = 0, a(A153880(n)) = A255411(a(n)), a(A273670(n)) = A256450(a(n)).

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Formula

A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2a(h).

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A273666 Permutation of nonnegative integers: a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

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Author

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Formula

cp's OEIS Frontend

A273667 Permutation of nonnegative integers: a(0) = 0, a(A153880(n)) = A255411(a(n)), a(A273670(n)) = A256450(a(n)).

Views

Author

Keywords

Links

Crossrefs

Formula

A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2*a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2*a(h).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A273666 Permutation of nonnegative integers: a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2a(h).