A345237 a(n) = Apex of XOR-triangle based on A346298(0..n).

0, 1, 2, 7, 3, 5, 4, 14, 16, 23, 24, 10, 30, 6, 1, 36, 22, 30, 60, 37, 9, 13, 5, 53, 70, 92, 121, 39, 67, 105, 9, 108, 128, 160, 152, 132, 190, 210, 176, 105, 221, 157, 147, 208, 151, 16, 99, 116, 225, 139, 25, 20, 72, 67, 156, 52, 508, 467, 257, 440, 276, 439, 33, 11

Offset

0,3

Comments

This sequence is not a permutation of nonnegative integers, example a(1) = a(14) = 1.

Row 1 of the XOR-triangle is the smallest number such that there is no duplicated value in any row of this triangle.

Links

Table of n, a(n) for n=0..63.

Formula

a(2^n) = A346298(2^n).

a(2^n + m) XOR a(m) = A346298(2^p + q) XOR A346298(q) if 2^n + m = 2^p + q.

a(n) <> a(n + 2^m + 2^p).

Example

Example for a(8):
Row 9:                 16 ...  = a(8)
                       / \
Row 8:               14  30 ...
                     / \ / \
Row 7:              4  10  20 ...
                   / \ / \ / \
Row 6:            5   1  11  31 ...
                 / \ / \ / \ / \
Row 5:          3   6   7  12  19 ...
               / \ / \ / \ / \ / \
Row 4:        7   4   2   5   9  26 ...
             / \ / \ / \ / \ / \ / \
Row 3:      2   5   1   3   6  15  21 ...
           / \ / \ / \ / \ / \ / \ / \
Row 2:    1   3   6   7   4   2  13  24 ...
         / \ / \ / \ / \ / \ / \ / \ / \
Row 1:  0   1   2   4   3   7   5   8  16 ...
       ---------------------------------------
Row 1 is A346298(0), ..., A346298(8)
Row 2 is A346298(0) XOR A346298(1), ..., A346298(7) XOR A346298(8)
Row 9: a(8)

Crossrefs

Cf. A346298.

Sequence in context: A326661 A326662 A345038 * A011049 A365768 A330883

Adjacent sequences: A345234 A345235 A345236 * A345238 A345239 A345240

Keyword

nonn,base

Author

Thomas Scheuerle, Jul 14 2021

Status

approved