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.

Showing 1-4 of 4 results.

A257738 Permutation of natural numbers: a(n) = A257726(A257690(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 25, 14, 33, 16, 17, 18, 35, 20, 13, 45, 23, 24, 115, 26, 47, 28, 19, 59, 15, 32, 163, 34, 146, 36, 51, 61, 39, 27, 78, 22, 723, 44, 203, 46, 182, 48, 43, 66, 67, 81, 53, 38, 101, 30, 856, 58, 251, 60, 226, 62, 63, 57, 86, 88, 1093, 104, 273, 70, 52, 128, 6093, 41, 223, 1010, 77
Offset: 1

Views

Author

Antti Karttunen, May 09 2015

Keywords

Links

Crossrefs

Inverse: A257737.
Cf. A257690, A257726, A257736.

Programs

Formula

a(n) = A257726(A257690(n)).

A257736 Permutation of natural numbers: a(n) = A257690(A257726(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 11, 10, 23, 12, 15, 14, 31, 16, 9, 22, 27, 20, 47, 46, 191, 24, 13, 30, 63, 28, 29, 62, 159, 32, 19, 18, 59, 44, 55, 54, 351, 40, 95, 94, 511, 92, 383, 382, 311, 48, 21, 26, 255, 60, 127, 126, 703, 56, 17, 58, 83, 124, 319, 318, 879, 64, 39, 38, 175, 36, 119, 118, 1919, 88, 111, 110, 1279, 108, 125
Offset: 1

Views

Author

Antti Karttunen, May 09 2015

Keywords

Links

Crossrefs

Inverse: A257735.
Cf. A257726, A257690, A257738.

Programs

Formula

a(n) = A257690(A257726(n)).

A257725 Permutation of natural numbers: a(0) = 0, a(lucky(n)) = 1 + 2*a(n-1), a(unlucky(n)) = 2*a(n), where lucky(n) = n-th lucky number A000959, unlucky(n) = n-th unlucky number A050505.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 5, 12, 7, 16, 10, 24, 9, 14, 13, 32, 20, 48, 18, 28, 17, 26, 64, 40, 11, 96, 36, 56, 34, 52, 25, 128, 15, 80, 22, 192, 33, 72, 112, 68, 104, 50, 21, 256, 30, 160, 44, 384, 49, 66, 19, 144, 224, 136, 208, 100, 42, 512, 60, 320, 88, 768, 29, 98, 132, 38, 27, 288, 65, 448, 272, 416, 41, 200, 97, 84, 1024, 120, 37
Offset: 0

Views

Author

Antti Karttunen, May 06 2015

Keywords

Comments

In other words, after a(0) = 0, if n is the k-th lucky number [i.e., n = A000959(k)], a(n) = 1 + 2*a(k-1); otherwise, when n is the k-th unlucky number [i.e., n = A050505(k)], a(n) = 2*a(k).
Because all lucky numbers are odd, it means that odd numbers occur in odd positions only (together with some even numbers, for each one of which there is a separate infinite cycle), while the even positions contain only even numbers.

Links

Crossrefs

Inverse: A257726.
Cf. A005408, A005843, A000959, A050505, A109497, A145649.
Related or similar permutations: A237427, A246377, A257732, A257734.
Cf. also A257690 (another similar permutation, but with a slightly different definition, resulting the first differing term at n=13, where a(13) = 9, while A257690(13) = 11).
Cf. also A257735 - A257738.

Formula

a(0) = 0; for n >= 1: if A145649(n) = 1 [i.e., if n is lucky], then a(n) = 1+(2*a(A109497(n)-1)), otherwise a(n) = 2*a(n-A109497(n)). [Where A109497(n) gives the number of lucky numbers <= n.]
As a composition of other permutations. For all n >= 1:
a(n) = A246377(A257732(n)).
a(n) = A237427(A257734(n)).

Extensions

Formula in name corrected by Antti Karttunen, Jan 10 2016

A183089 Tree generated by the lucky numbers: a(1) = 1; a(2n) = unlucky(a(n)), a(2n+1) = lucky(a(n+1)), where lucky = A000959, unlucky = A050505.

Original entry on oeis.org

1, 2, 3, 4, 7, 5, 9, 6, 21, 11, 13, 8, 31, 14, 15, 10, 87, 29, 37, 17, 49, 19, 25, 12, 141, 42, 51, 20, 63, 22, 33, 16, 517, 112, 133, 40, 189, 50, 69, 24, 259, 64, 75, 27, 111, 35, 43, 18, 925, 177, 211, 56, 267, 66, 79, 28, 339, 83, 93, 30, 159, 45, 67, 23, 4129, 618, 685, 143, 855, 167, 201, 54, 1275, 234, 261, 65, 391, 90, 105, 34
Offset: 1

Views

Author

Clark Kimberling, Dec 24 2010

Keywords

Comments

A permutation of the positive integers. See the comment at A183079.

Examples

			Top 6 levels of the binary tree:
                                     1
                                     |
                  ...................2...................
                 3                                       4
       7......../ \........5                   9......../ \........6
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  21       11         13       8          31       14         15       10
87  29   37  17     49  19   25 12     141  42   51  20     63  22   33  16
...
From the level 3 to the level 4: 3 --> (7,5) and 4 --> (9,6).

Links

Crossrefs

Inverse permutation: A257690.
Cf. A000959, A050505.
Cf. A257726 (similar permutation with a slightly different definition, resulting the first differing term at n=9, where a(9) = 21, while A257726(9) = 13), A257735 - A257738.
Cf. A183079, A237739 (other similar permutations).

Formula

Let L(n) = A000959(n), the n-th lucky number.
Let U(n) = A050505(n), the n-th unlucky numbers.
The tree-array T(n,k) is then given by rows:
T(0,0) = 1; T(1,0) = 2;
T(n,2j) = L(T(n-1),j);
T(n,2j+1) = U(T(n-1),j);
for j = 0, 1, ..., 2^(n-1) - 1, n >= 2.
a(1) = 1; a(2n) = A050505(a(n)), a(2n+1) = A000959(a(n+1)). - Antti Karttunen, May 09 2015

Extensions

Added a formula to the Name field and more terms, edited Example section - Antti Karttunen, May 09 2015
Showing 1-4 of 4 results.

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