A268711 -id:A268711 - cp's OEIS frontend

A268680 Least monotonic left inverse of A268678.

0, 1, 1, 2, 3, 4, 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 14, 14, 15, 16, 16, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 21, 22, 23, 24, 24, 24, 24, 24, 25, 26, 26, 27, 27, 28, 29, 29, 29, 30, 31, 31, 32, 33, 33, 33, 33, 34, 35, 36, 36, 36, 37, 38, 38, 39, 39, 40, 41, 41, 41, 41, 41, 41, 42, 43, 44

Offset: 0

Antti Karttunen, Feb 11 2016

nonn

a(n) = number of distinct nonzero values A268395 that occur in range [0 .. n].

Each n occurs A268679(n+1) times.

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A268678, A268679, A268395.

Cf. also A268711.

Other identities. For all n >= 0:

a(A268678(n)) = n.

A268712 Permutation of natural numbers: a(1) = 1, a(2n) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).

Original entry on oeis.org

1, 2, 3, 6, 4, 9, 5, 13, 11, 10, 7, 21, 18, 12, 8, 29, 23, 25, 20, 24, 19, 14, 15, 45, 40, 39, 34, 28, 22, 17, 16, 62, 56, 49, 42, 54, 48, 44, 37, 51, 47, 43, 36, 30, 26, 33, 27, 95, 87, 84, 75, 80, 74, 73, 65, 61, 53, 46, 41, 38, 32, 35, 31, 129, 120, 115, 108, 100, 93, 88, 82, 112, 105, 99, 92, 94, 86, 78, 70

Offset: 1

Antti Karttunen, Feb 11 2016

This sequence can be represented as a binary tree. Each left hand child is produced as A268677(n), and each right hand child as A268678(1+n), when the parent node contains n:
                                     |
                  ...................1...................
                 2                                       3
       6......../ \........4                   9......../ \........5
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  13       11         10       7          21       18         12       8
29 23    25  20     24  19   14 15      45  40   39  34     28  22   17 16
etc.

Antti Karttunen, Table of n, a(n) for n = 1..16383
Index entries for sequences that are permutations of the natural numbers

Inverse: A268711.

Cf. A268677, A268678.

a(1) = 1, after which: a(2n) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).

cp's OEIS Frontend

A268680 Least monotonic left inverse of A268678.

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