A269391 -id:A269391 - cp's OEIS frontend

A269401 Permutation of natural numbers: a(1) = 1, a(A179016(1+n)) = 2a(n), a(A213713(n)) = 1 + 2a(n), where A179016 is the infinite trunk of binary beanstalk and A213713 is its complement.

1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 11, 9, 25, 10, 8, 27, 31, 24, 29, 23, 19, 26, 51, 21, 30, 17, 55, 63, 49, 28, 22, 59, 47, 18, 39, 53, 103, 50, 43, 61, 20, 35, 111, 127, 16, 99, 57, 54, 45, 119, 95, 62, 37, 79, 107, 48, 207, 101, 87, 123, 41, 58, 46, 71, 223, 38, 255, 33, 199, 52, 115, 109, 102, 91, 239, 191, 42, 125, 75, 60

Offset: 1

Antti Karttunen, Mar 05 2016

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Inverse: A269402.
Cf. A179016, A213713, A213719, A269371.
Related or similar permutations: A269391, A269398.

a(1) = 1, for n > 1, if A213719(n) = 1 [when n is in A179016] a(n) = 2*a(A269371(n)-1), otherwise a(n) = 1 + 2*a(n-A269371(n)).
As a composition of other permutations:
a(n) = A269391(A269398(n)).

A269381 Least monotonic left inverse of A233271.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26

Offset: 0

Antti Karttunen, Mar 05 2016

nonn

a(n) = number of nonzero terms of A233271 <= n.

Antti Karttunen, Table of n, a(n) for n = 0..8192

Cf. A233271.

Cf. also A269391.

nn = 90; s = NestList[# + 1 + DigitCount[#, 2, 0] &, 1, nn]; Table[Count[Take[s, n + 1], k_ /; k <= n], {n, 0, nn}]  (* Michael De Vlieger, Mar 07 2016, after Harvey P. Dale at A216431 *)

Other identities. For all n >= 0:

a(A233271(n)) = n.

A269390 Complement of A233271.

Original entry on oeis.org

3, 5, 6, 9, 10, 11, 13, 14, 17, 18, 19, 20, 22, 23, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 83, 84, 85, 86, 88, 89, 91, 92, 93, 95, 96, 98, 99, 100, 101, 103, 104, 105, 107, 108, 109, 111

Offset: 1

Antti Karttunen, Mar 05 2016

Antti Karttunen, Table of n, a(n) for n = 1..13890

Cf. A233271 (complement).
Cf. A269381.
Cf. also A213713, A269391, A269392.

A269392 Permutation of natural numbers: a(1) = 1, a(2n) = A233271(1+a(n)), a(2n+1) = A269390(a(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 8, 9, 12, 10, 16, 13, 15, 11, 21, 14, 24, 17, 32, 20, 28, 18, 49, 26, 38, 22, 46, 25, 31, 19, 64, 34, 42, 23, 79, 37, 53, 27, 110, 48, 63, 33, 94, 43, 56, 29, 186, 72, 87, 40, 128, 57, 71, 35, 174, 68, 82, 39, 106, 47, 60, 30, 245, 92, 117, 51, 152, 62, 75, 36, 322, 112, 127, 55, 203, 77, 90, 41

Offset: 1

Antti Karttunen, Mar 05 2016

This sequence can be represented as a binary tree. Each left hand child is produced as A233271(1+n), and each right hand child as A269390(n), when the parent contains n:
                                    |
                 ...................1...................
                2                                       3
      4......../ \........5                   7......../ \........6
     / \                 / \                 / \                 / \
    /   \               /   \               /   \               /   \
   /     \             /     \             /     \             /     \
  8       9          12       10         16       13         15       11
21 14   24 17      32  20   28  18     49  26   38  22     46  25   31  19
etc.

Antti Karttunen, Table of n, a(n) for n = 1..3071
Index entries for sequences that are permutations of the natural numbers

Inverse: A269391.
Cf. A233271, A269390.
Cf. also A260432.
Similar or related permutations: A269398, A269402.

a(1) = 1, a(2n) = A233271(1+a(n)), a(2n+1) = A269390(a(n)).
As a composition of other permutations:
a(n) = A269398(A269402(n)).

A269397 Permutation of natural numbers: a(1) = 1, a(A233271(1+n)) = A179016(1+a(n)), a(A269390(n)) = A213713(a(n)), where A179016, A233271 are the infinite trunks of binary beanstalk and inverted binary beanstalk and A213713, A269390 their complements.

Original entry on oeis.org

1, 3, 2, 7, 6, 5, 4, 16, 13, 12, 10, 15, 9, 27, 11, 8, 22, 21, 18, 25, 46, 17, 43, 35, 20, 14, 36, 32, 34, 29, 26, 42, 40, 69, 28, 65, 54, 23, 33, 24, 55, 85, 50, 52, 45, 31, 41, 62, 19, 60, 100, 44, 67, 95, 80, 64, 37, 51, 38, 53, 82, 122, 78, 158, 75, 77, 68, 48, 61, 91, 49, 30, 88, 143, 145, 66, 98, 136, 116, 115, 93, 63, 56, 76, 58, 79, 39

Offset: 1

Antti Karttunen, Mar 05 2016

Antti Karttunen, Table of n, a(n) for n = 1..8191
Antti Karttunen, Entanglement Permutations, 2016-2017
Index entries for sequences that are permutations of the natural numbers

Inverse: A269398.
Cf. A179016, A213713, A233271, A269381, A269390.
Related or similar permutations: A269391, A269401, A269402.
Cf. also A233270.

a(1) = 1, for n > 1, if A269381(n) - A269381(n-1) > 0 [when n is in A233271] a(n) = A179016(1+a(A269381(n)-1)), otherwise a(n) = A213713(a(n-A269381(n))).
As a composition of related permutations:
a(n) = A269402(A269391(n)).

cp's OEIS Frontend

A269401 Permutation of natural numbers: a(1) = 1, a(A179016(1+n)) = 2a(n), a(A213713(n)) = 1 + 2a(n), where A179016 is the infinite trunk of binary beanstalk and A213713 is its complement.

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A269381 Least monotonic left inverse of A233271.

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A269390 Complement of A233271.

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A269392 Permutation of natural numbers: a(1) = 1, a(2n) = A233271(1+a(n)), a(2n+1) = A269390(a(n)).

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A269397 Permutation of natural numbers: a(1) = 1, a(A233271(1+n)) = A179016(1+a(n)), a(A269390(n)) = A213713(a(n)), where A179016, A233271 are the infinite trunks of binary beanstalk and inverted binary beanstalk and A213713, A269390 their complements.

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cp's OEIS Frontend

A269401 Permutation of natural numbers: a(1) = 1, a(A179016(1+n)) = 2*a(n), a(A213713(n)) = 1 + 2*a(n), where A179016 is the infinite trunk of binary beanstalk and A213713 is its complement.

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Author

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Formula

A269381 Least monotonic left inverse of A233271.

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Comments

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Programs

Mathematica

Formula

A269390 Complement of A233271.

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A269392 Permutation of natural numbers: a(1) = 1, a(2n) = A233271(1+a(n)), a(2n+1) = A269390(a(n)).

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Author

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Comments

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Crossrefs

Formula

A269397 Permutation of natural numbers: a(1) = 1, a(A233271(1+n)) = A179016(1+a(n)), a(A269390(n)) = A213713(a(n)), where A179016, A233271 are the infinite trunks of binary beanstalk and inverted binary beanstalk and A213713, A269390 their complements.

Views

Author

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Links

Crossrefs

Formula

A269401 Permutation of natural numbers: a(1) = 1, a(A179016(1+n)) = 2a(n), a(A213713(n)) = 1 + 2a(n), where A179016 is the infinite trunk of binary beanstalk and A213713 is its complement.