A269383 -id:A269383 - cp's OEIS frontend

A269384 Permutation of natural numbers: a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.

1, 2, 3, 4, 5, 8, 7, 6, 9, 14, 15, 18, 13, 20, 11, 10, 17, 26, 27, 34, 29, 44, 35, 30, 25, 38, 39, 48, 21, 32, 19, 12, 33, 50, 51, 64, 53, 80, 67, 58, 57, 86, 87, 108, 69, 104, 59, 54, 49, 74, 75, 94, 77, 116, 95, 84, 41, 62, 63, 78, 37, 56, 23, 16, 65, 98, 99, 124, 101, 152, 127, 112, 105, 158, 159, 198, 133, 200

Offset: 1

Antti Karttunen, Mar 01 2016

Permutation obtained from the Ludic 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 A269382(n), when the parent node contains n:
                                    1
                                    |
                 ...................2...................
                3                                       4
      5......../ \........8                   7......../ \........6
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  9       14         15       18         13       20         11       10
17 26   27  34     29  44   35  30     25  38   39  48     21  32   19  12
etc.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A269383.
Cf. A000035, A001511, A003602, A255127, A269382.
Cf. also A269385, A269387 and also A249814, A269374.

a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.
a(1) = 1, a(2n) = A269382(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.]

A269373 Permutation of natural numbers: a(1) = 1, a(n) = A000079(A260438(n+1)-1) * ((2 * a(A260439(n+1))) - 1).

Original entry on oeis.org

1, 2, 3, 6, 5, 4, 11, 8, 9, 10, 7, 16, 21, 32, 15, 22, 17, 12, 19, 64, 13, 18, 31, 128, 41, 24, 63, 14, 29, 256, 43, 512, 33, 42, 23, 1024, 37, 20, 127, 30, 25, 2048, 35, 48, 61, 34, 255, 4096, 81, 8192, 47, 38, 125, 96, 27, 40, 57, 26, 511, 44, 85, 16384, 1023, 62, 65, 32768, 83, 65536, 45, 82, 2047, 131072, 73, 262144, 39

Offset: 1

Antti Karttunen, Mar 01 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..1024
Index entries for sequences that are permutations of the natural numbers

Inverse: A269374.
Cf. A000035, A000079, A260438, A260439.
Cf. also A249813, A269383.

a(1) = 1, a(n) = A000079(A260438(n+1)-1) * ((2 * a(A260439(n+1))) - 1).
Other identities. For all n >= 0:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]

cp's OEIS Frontend

A269384 Permutation of natural numbers: a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.

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