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

Author

Thomas Scheuerle, Jul 14 2021

Keywords

• nonn
• base

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.

Examples

			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.

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).