A269369 -id:A269369 - cp's OEIS frontend

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)).

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

Antti Karttunen, Mar 01 2016

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.

Antti Karttunen, Table of n, a(n) for n = 0..4095
Index entries for sequences that are permutations of the natural numbers

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.

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.]

A269377 Tree of Lucky sieve: a(0) = 1, a(1) = 2; after which a(2n) = A269369(a(n)), a(2n+1) = 2*a(n).

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 11, 12, 19, 10, 17, 16, 13, 18, 35, 28, 39, 22, 29, 24, 27, 38, 23, 20, 61, 34, 41, 32, 15, 26, 47, 36, 123, 70, 77, 56, 57, 78, 59, 44, 103, 58, 65, 48, 45, 54, 107, 76, 81, 46, 53, 40, 91, 122, 95, 68, 145, 82, 89, 64, 21, 30, 71, 52, 165, 94, 101, 72, 183, 246, 203, 140, 271, 154, 161, 112, 97

Offset: 0

Antti Karttunen, Mar 01 2016

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. After a(1)=2, each left hand child is obtained by applying A269369 to the parent, and each right hand child is obtained by doubling the contents of the parent node, when the parent node contains n:
                                    1
                                    |
                 ...................2...................
                3                                       4
      7......../ \........6                   5......../ \........8
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  9       14         11       12         19       10         17       16
13 18   35  28     39  22   29  24     27  38   23  20     61  34   41  32
etc.
Sequence A269375 is obtained from the mirror image of the same tree.

Antti Karttunen, Table of n, a(n) for n = 0..4095
Index entries for sequences that are permutations of the natural numbers

Inverse: A269378.
Cf. A269369.
Cf. A000959 (with 2 inserted between 1 and 3 forms the left edge of the tree).
Related permutation: A269375.
Cf. also A252753, A269387.

a(0) = 1, a(1) = 2; after which, a(2n) = A269369(a(n)), a(2n+1) = 2*a(n).
As a composition of related permutations:
a(n) = A260742(A269387(n)).

A269372 Permutation of even numbers: a(n) = A269369(n+1) - 1.

Original entry on oeis.org

0, 2, 6, 4, 18, 10, 8, 16, 12, 22, 38, 28, 14, 34, 20, 40, 60, 46, 26, 52, 24, 58, 80, 64, 30, 70, 44, 76, 102, 82, 32, 88, 36, 94, 122, 100, 42, 106, 56, 112, 144, 118, 48, 124, 54, 130, 164, 136, 50, 142, 62, 148, 186, 154, 84, 160, 96, 166, 206, 172, 90, 178, 66, 184, 228, 190, 68, 196, 72, 202, 248, 208, 74

Offset: 0

Antti Karttunen, Mar 01 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 0..11011

Cf. A269369, A269374.

Cf. also A253886, A269382.

(define (A269372 n) (- (A269369 (+ 1 n)) 1))

a(n) = A269369(1+n) - 1.

A270195 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269369(1+a(n)).

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 5, 8, 19, 14, 17, 12, 9, 10, 11, 16, 13, 38, 53, 28, 21, 34, 47, 24, 15, 18, 23, 20, 39, 22, 29, 32, 61, 26, 35, 76, 57, 106, 155, 56, 103, 42, 59, 68, 123, 94, 137, 48, 31, 30, 41, 36, 27, 46, 65, 40, 25, 78, 113, 44, 81, 58, 83, 64, 37, 122, 179, 52, 45, 70, 101, 152, 271, 114, 167, 212, 375, 310, 461, 112, 97

Offset: 1

Antti Karttunen, Mar 13 2016

This sequence can be represented as a binary tree. When the parent contains n, the left hand child contains 2n, while the value of right hand child is obtained by applying A269369(1+n):
                                    1
                                    |
                 ................../ \..................
                2                                       3
      4......../ \........7                   6......../ \........5
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  8       19         14       17         12       9          10       11
16 13   38  53     28  21   34  47     24  15   18 23      20  39   22  29
etc.

Antti Karttunen, Table of n, a(n) for n = 1..8191
Index entries for sequences that are permutations of the natural numbers

Inverse: A270196.
Cf. A269369.
Related or similar permutations: A269865, A269374, A269375, A270197.

a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269369(1+a(n)).

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

Antti Karttunen, Mar 13 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8191
Index entries for sequences that are permutations of the natural numbers

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

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).

A270197 Self-inverse permutation of natural numbers: a(1) = 1, for n even, a(n) = A269369(1+a(n/2)), for n odd, a(n) = 2*a(A269370(n)-1).

Original entry on oeis.org

1, 3, 2, 5, 4, 7, 6, 11, 14, 19, 8, 17, 22, 9, 34, 29, 12, 21, 10, 53, 18, 13, 28, 47, 106, 81, 42, 23, 16, 123, 94, 83, 246, 15, 44, 59, 166, 39, 38, 155, 68, 27, 118, 35, 162, 103, 24, 137, 54, 375, 274, 239, 20, 49, 70, 65, 78, 61, 36, 365, 58, 333, 750, 245, 56, 403, 666, 41, 806, 55, 212, 173, 82, 585, 346, 113, 84, 57, 1170, 461, 26, 73, 32

Offset: 1

Antti Karttunen, Mar 13 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..2211
Index entries for sequences that are permutations of the natural numbers

Cf. A269369, A269370.

Similar or related permutations A270195, A270196, A269867.

a(1) = 1, for n even, a(n) = A269369(1+a(n/2)), for n odd, a(n) = 2*a(A269370(n)-1).

A269379 a(1) = 1; for n > 1, a(n) = A255127(A260738(n)+1, A260739(n)).

Original entry on oeis.org

1, 3, 5, 9, 7, 15, 11, 21, 19, 27, 13, 33, 17, 39, 35, 45, 23, 51, 31, 57, 49, 63, 25, 69, 29, 75, 65, 81, 37, 87, 55, 93, 79, 99, 59, 105, 41, 111, 95, 117, 43, 123, 47, 129, 109, 135, 53, 141, 85, 147, 125, 153, 61, 159, 73, 165, 139, 171, 103, 177, 67, 183, 155, 189, 113, 195, 71, 201, 169, 207, 77, 213, 101, 219, 185, 225, 83

Offset: 1

Antti Karttunen, Mar 01 2016

nonn

a(n) = the number located immediately below n in A255127 (square array generated by Ludic sieve) in the same column where n itself is, or in other words, the number removed in the next filtering stage at the same step as when n was removed in the A260738(n)-th stage.

Permutation of odd numbers.

Antti Karttunen, Table of n, a(n) for n = 1..32999

Cf. A255127, A260738, A260739.
Cf. A269171, A269356, A269358, A269382, A269385, A269387 (sequences that use this function).
Cf. A269380 (left inverse).
Cf. also A250469, A269369.

(define (A269379 n) (if (= 1 n) n (A255127bi (+ (A260738 n) 1) (A260739 n)))) ;; Code for A255127bi given in A255127.

a(1) = 1; for n > 1, a(n) = A255127(A260738(n)+1, A260739(n)).
Other identities. For all n >= 1:
A269380(a(n)) = n.

A269370 a(1) = 1, after which, for odd n: a(n) = A260439(n)-th number k for which A260438(k) = A260438(n)-1, and for even n: a(n) = a(n/2).

Original entry on oeis.org

1, 1, 2, 1, 4, 2, 3, 1, 7, 4, 6, 2, 9, 3, 13, 1, 8, 7, 5, 4, 15, 6, 10, 2, 21, 9, 19, 3, 12, 13, 25, 1, 31, 8, 14, 7, 33, 5, 11, 4, 16, 15, 37, 6, 27, 10, 18, 2, 43, 21, 49, 9, 20, 19, 45, 3, 39, 12, 22, 13, 17, 25, 51, 1, 24, 31, 63, 8, 67, 14, 26, 7, 69, 33, 73, 5, 28, 11, 75, 4, 23, 16, 30, 15, 55, 37, 79, 6, 32, 27, 61, 10, 87, 18, 34, 2

Offset: 1

Antti Karttunen, Mar 01 2016

nonn

For odd numbers n > 1, a(n) tells which term is on the immediately preceding row of A255551 (square array generated by Lucky sieve), in the same column where n itself is.

Antti Karttunen, Table of n, a(n) for n = 1..11017

Cf. A255551, A260438, A260439, A269369.

Cf. also A268674, A269380.

(define (A269370 n) (cond ((= 1 n) n) ((even? n) (A269370 (/ n 2))) (else (A255551bi (- (A260438 n) 1) (A260439 n))))) ;; Code for A255551bi given in A255551.

a(1) = 1; after which for even n, a(n) = a(n/2), and for odd n, a(n) = A255551(A260438(n)-1, A260439(n)).
Other identities. For all n >= 1:
a(A269369(n)) = n.

cp's OEIS Frontend

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)).

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A269377 Tree of Lucky sieve: a(0) = 1, a(1) = 2; after which a(2n) = A269369(a(n)), a(2n+1) = 2*a(n).

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A269372 Permutation of even numbers: a(n) = A269369(n+1) - 1.

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A270195 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269369(1+a(n)).

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

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A270197 Self-inverse permutation of natural numbers: a(1) = 1, for n even, a(n) = A269369(1+a(n/2)), for n odd, a(n) = 2*a(A269370(n)-1).

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A269379 a(1) = 1; for n > 1, a(n) = A255127(A260738(n)+1, A260739(n)).

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A269370 a(1) = 1, after which, for odd n: a(n) = A260439(n)-th number k for which A260438(k) = A260438(n)-1, and for even n: a(n) = a(n/2).

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