cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A279342 a(0) = 1, a(1) = 2, a(2n) = A055938(a(n)), a(2n+1) = A005187(a(n)).

Original entry on oeis.org

1, 2, 5, 3, 12, 8, 6, 4, 27, 22, 17, 15, 13, 10, 9, 7, 58, 50, 45, 41, 36, 32, 30, 26, 28, 23, 21, 18, 20, 16, 14, 11, 121, 112, 103, 97, 92, 86, 84, 79, 75, 70, 65, 63, 61, 56, 55, 49, 59, 53, 48, 42, 44, 39, 37, 34, 43, 38, 33, 31, 29, 25, 24, 19, 248, 237, 227, 221, 210, 201, 196, 191, 187, 180, 175, 168, 171, 165, 160, 153, 154, 146, 141
Offset: 0

Views

Author

Antti Karttunen, Dec 10 2016

Keywords

Comments

Note the indexing: the domain starts from 0, while the range excludes zero.
This sequence can be represented as a binary tree. Each left hand child is produced as A055938(n), and each right hand child as A005187(n), when the parent node contains n:
1
|
...................2...................
5 3
12......../ \........8 6......../ \........4
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
27 22 17 15 13 10 9 7
58 50 45 41 36 32 30 26 28 23 21 18 20 16 14 11
etc.

Links

Crossrefs

Inverse: A279341.
Right edge: A256994.
Cf. A005187, A055938.
Related or similar permutations: A054429, A163511, A233278, A256997, A279339, A279344, A279347.

Programs

Formula

a(0) = 1, a(1) = 2, and then after, a(2n) = A055938(a(n)), a(2n+1) = A005187(a(n)).
As a composition of other permutations:
a(n) = A279344(A054429(n)).
a(n) = A279347(A279344(n)).
a(n) = A279339(A163511(n)).

A276442 Permutation of natural numbers: a(1) = 1; a(2n) = A088359(a(n)), a(2n+1) = A087686(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 3, 2, 6, 7, 5, 4, 11, 14, 13, 15, 10, 12, 9, 8, 20, 26, 25, 30, 23, 29, 28, 31, 19, 24, 22, 27, 18, 21, 17, 16, 37, 47, 46, 57, 44, 56, 55, 62, 41, 53, 52, 61, 50, 60, 59, 63, 36, 45, 43, 54, 40, 51, 49, 58, 35, 42, 39, 48, 34, 38, 33, 32, 70, 85, 84, 105, 82, 104, 103, 120, 79, 101, 100, 119, 98, 118, 117, 126, 75, 95, 94
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A088359(n), and each right hand child as A087686(1+n), when their parent contains n:
|
...................1...................
3 2
6......../ \........7 5......../ \........4
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
11 14 13 15 10 12 9 8
20 26 25 30 23 29 28 31 19 24 22 27 18 21 17 16
etc.
As in the mirror image permutation A267112, the level k of the tree contains all numbers of binary width k like many other base-2 related permutations (A003188, A054429, A233278, etc). For a proof, see A267110, which gives the contents of each parent node (for a node containing n > 1).

Links

Crossrefs

Inverse: A276441.
Cf. A004001, A087686, A088359, A267110.
Related or similar permutations: A003188, A054429, A233276, A233278, A267112, A276344, A276346, A276444.

Programs

Formula

a(1) = 1; after which, a(2n) = A088359(a(n)), a(2n+1) = A087686(1+a(n)).
As a composition of other permutations:
a(n) = A267112(A054429(n)).
a(n) = A276344(A233278(n)).
a(n) = A276346(A233276(n)).
a(n) = A276444(A003188(n)).

A276343 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = A005187(1+a(n)), a(A088359(n)) = A055938(a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12, 11, 9, 10, 8, 31, 30, 29, 28, 27, 26, 24, 20, 25, 21, 23, 22, 17, 18, 19, 16, 63, 62, 61, 60, 59, 58, 57, 55, 51, 43, 56, 52, 44, 54, 48, 53, 50, 45, 36, 47, 37, 39, 49, 40, 41, 46, 42, 33, 34, 35, 38, 32, 127, 126, 125, 124, 123, 122, 121, 120, 118, 114, 106, 90, 119, 115, 107, 91, 117, 111, 99
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276344.
Cf. A004001, A005187, A055938, A080677, A087686, A088359, A093879.
Similar or related permutations: A233276, A233278, A267111, A276345, A276441.
Compare also to the scatter-plots of A276443 and A276445.

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A005187(1+a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A055938(a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A233276(A267111(n)).
a(n) = A233278(A276441(n)).

A276345 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = A055938(a(n)), a(A088359(n)) = A005187(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 2, 3, 5, 4, 7, 6, 12, 10, 8, 15, 9, 11, 14, 13, 27, 23, 19, 16, 31, 21, 18, 22, 17, 26, 30, 20, 25, 24, 29, 28, 58, 53, 46, 38, 32, 63, 48, 41, 35, 42, 40, 34, 50, 33, 57, 62, 44, 39, 49, 37, 47, 45, 36, 56, 55, 61, 43, 54, 52, 51, 60, 59, 121, 113, 104, 89, 74, 64, 127, 108, 95, 81, 70, 82, 93, 79, 67, 98, 77, 66, 112, 65, 120
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276346.
Cf. A004001, A005187, A055938, A080677, A087686, A088359, A093879.
Similar or related permutations: A233276, A233278, A267111, A276343, A276441.

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A055938(a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A005187(1+a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A233276(A276441(n)).
a(n) = A233278(A267111(n)).

A257249 a(0) = 1, and for n >= 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 2, 1, 2, 3, 3, 2, 4, 3, 2, 1, 2, 3, 3, 3, 4, 4, 2, 4, 3, 3, 2, 5, 4, 3, 2, 1, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 2, 5, 5, 3, 4, 3, 5, 3, 2, 4, 4, 5, 4, 3, 3, 2, 6, 5, 4, 3, 2, 1, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 3, 5, 5, 4, 4, 4, 5, 4, 2, 5, 5, 5, 5, 3, 3, 4, 6, 6, 4, 5, 3, 5, 4, 3, 2, 6, 4, 4, 4, 3, 5, 4, 5, 5, 6, 3, 3, 5, 2, 6, 4, 4, 5, 4, 3, 3, 2, 7, 6, 5, 4, 3, 2, 1, 2
Offset: 0

Views

Author

Antti Karttunen, Apr 19 2015

Keywords

Comments

Because A233275(n) = A003188(n) for n = 1 .. 9, a(n) = A005811(n) for n = 1 .. 9.

Links

Crossrefs

One more than A256479.
Cf. A000120, A003188, A005811, A055938, A070939, A079559, A080791, A213714, A234017, A233275, A233277, A233278, A257248, A256991.

Formula

a(0) = 1, and for n >= 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).
Other identities. For all n >= 1:
a(n) = A070939(n) - A257248(n).
a(n) = A000120(A233275(n)). [Binary weight of A233275(n).]
a(n) = 1 + A256479(n) = 1 + A080791(A233277(n)).
Previous Showing 11-15 of 15 results.

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