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.

A269375 Tree of Lucky sieve, mirrored: a(0) = 1, a(1) = 2; after which a(2n) = 2*a(n), a(2n+1) = A269369(a(n)).

Original entry on oeis.org

1, 2, 4, 3, 8, 5, 6, 7, 16, 17, 10, 19, 12, 11, 14, 9, 32, 41, 34, 61, 20, 23, 38, 27, 24, 29, 22, 39, 28, 35, 18, 13, 64, 89, 82, 145, 68, 95, 122, 91, 40, 53, 46, 81, 76, 107, 54, 45, 48, 65, 58, 103, 44, 59, 78, 57, 56, 77, 70, 123, 36, 47, 26, 15, 128, 185, 178, 313, 164, 239, 290, 217, 136, 197, 190, 333, 244, 359, 182, 147, 80
Offset: 0

Views

Author

Antti Karttunen, Mar 01 2016

Keywords

Comments

Permutation of natural numbers obtained from the Lucky sieve. Note the indexing: Domain starts from 0, range from 1.
This sequence can be represented as a binary tree. Each left hand child is obtained by doubling the parent's contents, and each right hand child is obtained by applying A269369 to the parent's contents:
1
|
...................2...................
4 3
8......../ \........5 6......../ \........7
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
16 17 10 19 12 11 14 9
32 41 34 61 20 23 38 27 24 29 22 39 28 35 18 13
etc.
Sequence A269377 is obtained from the mirror image of the same tree.

Links

Crossrefs

Inverse: A269376.
Cf. A000035, A269369.
Cf. A000959 (with 2 inserted between 1 and 3 forms the right edge of the tree).
Related or similar permutations: A163511, A260742, A269377.
Cf. also A252755, A269385.

Formula

a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A269369(a(n)).
As a composition of related permutations:
a(n) = A260742(A269385(n)).
Other identities. For all n >= 2:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n from a(2)=4 onward.]

A269386 Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A269380(2n+1)).

Original entry on oeis.org

0, 1, 3, 2, 7, 6, 15, 4, 5, 14, 31, 12, 63, 30, 13, 8, 127, 10, 11, 28, 9, 62, 255, 24, 511, 126, 29, 60, 1023, 26, 23, 16, 25, 254, 27, 20, 2047, 22, 61, 56, 4095, 18, 8191, 124, 17, 510, 16383, 48, 19, 1022, 21, 252, 32767, 58, 47, 120, 57, 2046, 55, 52, 65535, 46, 125, 32, 59, 50, 131071, 508, 49, 54, 262143, 40, 95, 4094, 253, 44
Offset: 1

Views

Author

Antti Karttunen, Mar 01 2016

Keywords

Comments

Note the indexing: Domain starts from 1, range from 0.

Links

Crossrefs

Inverse: A269385.
Cf. A269380.
Related permutations: A260742, A269172, A269388.
Cf. also A252756, A269376.
Differs from A243071 and A252756 for the first time at n=19, which here a(19) = 11, instead of 255.

Formula

a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A269380(2n+1)).
As a composition of related permutations:
a(n) = A252756(A269172(n)).
a(n) = A269376(A260742(n)).

A269378 Permutation of natural numbers: a(1) = 0, after which a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a(A269370(n)).

Original entry on oeis.org

0, 1, 2, 3, 6, 5, 4, 7, 8, 13, 10, 11, 16, 9, 32, 15, 14, 17, 12, 27, 64, 21, 26, 23, 128, 33, 24, 19, 22, 65, 256, 31, 512, 29, 18, 35, 1024, 25, 20, 55, 30, 129, 2048, 43, 48, 53, 34, 47, 4096, 257, 8192, 67, 54, 49, 96, 39, 40, 45, 42, 131, 28, 513, 16384, 63, 46, 1025, 32768, 59, 65536, 37, 66, 71, 131072, 2049, 262144, 51, 38, 41
Offset: 1

Views

Author

Antti Karttunen, Mar 01 2016

Keywords

Comments

Note the indexing: Domain starts from 1, range from 0.

Links

Crossrefs

Inverse: A269377.
Cf. A269370.
Related permutation: A269376.
Cf. also A252754, A269388.

Formula

a(1) = 0, after which, a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a(A269370(n)).
As a composition of related permutations:
a(n) = A269388(A260741(n)).

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

Views

Author

Antti Karttunen, Mar 13 2016

Keywords

Links

Crossrefs

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

Formula

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).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.