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A345237
a(n) = Apex of XOR-triangle based on A346298(0..n).
1
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.
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 A372131 A365768
KEYWORD
nonn,base
AUTHOR
Thomas Scheuerle, Jul 14 2021
STATUS
approved