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 1-3 of 3 results.

A269374 Permutation of natural numbers: a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.

Original entry on oeis.org

1, 2, 3, 6, 5, 4, 11, 8, 9, 10, 7, 18, 21, 28, 15, 12, 17, 22, 19, 38, 13, 16, 35, 26, 41, 58, 55, 102, 29, 40, 23, 14, 33, 46, 43, 80, 37, 52, 75, 56, 25, 34, 31, 60, 69, 100, 51, 44, 81, 118, 115, 206, 109, 160, 203, 152, 57, 82, 79, 144, 45, 64, 27, 20, 65, 94, 91, 164, 85, 124, 159, 120, 73, 106, 103, 186, 149, 220, 111, 96, 49
Offset: 1

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Author

Antti Karttunen, Mar 01 2016

Keywords

Comments

Permutation obtained from the Lucky sieve.
This sequence can be represented as a binary tree. For n > 2, each left hand child is obtained by doubling the contents of the parent node and subtracting one, and each right hand child is obtained by applying A269372(n), when the parent node contains n:
1
|
...................2...................
3 6
5......../ \........4 11......../ \........8
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
9 10 7 18 21 28 15 12
17 22 19 38 13 16 35 26 41 58 55 102 29 40 23 14
etc.

Links

Crossrefs

Inverse: A269373.
Cf. A000035, A001511, A003602, A255551, A269372.
Cf. also A269375, A269377 and also A249814, A269384.

Formula

a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.
a(1) = 1, a(2n) = A269372(a(n)), a(2n+1) = (2*a(n+1))-1.
Other identities. For all n >= 0:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of 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).

A269383 Permutation of natural numbers: a(1) = 1, a(n) = A000079(A260738(n+1)-1) * ((2 * a(A260739(n+1))) - 1).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 15, 32, 13, 10, 11, 64, 17, 12, 31, 14, 29, 128, 63, 256, 25, 18, 19, 512, 21, 24, 127, 30, 33, 20, 23, 1024, 61, 26, 27, 2048, 57, 4096, 255, 22, 125, 8192, 511, 28, 49, 34, 35, 16384, 37, 48, 1023, 62, 41, 40, 47, 32768, 253, 58, 59, 36, 65, 65536, 39, 126, 45, 131072, 2047, 96, 121, 50, 51, 262144, 53, 60
Offset: 1

Views

Author

Antti Karttunen, Mar 01 2016

Keywords

Links

Crossrefs

Inverse: A269384.
Cf. A000035, A000079, A260738, A260739.
Cf. also A249813, A269373.
Differs from both A246683 and A249813 for the first time at n=18, which here a(18)=12, instead of 128.

Formula

a(1) = 1, a(n) = A000079(A260738(n+1)-1) * ((2 * a(A260739(n+1))) - 1).
Other identities. For all n >= 0:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
Showing 1-3 of 3 results.

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

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