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%I #37 Aug 21 2021 16:24:54
%S 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,
%T 121,39,67,105,9,108,128,160,152,132,190,210,176,105,221,157,147,208,
%U 151,16,99,116,225,139,25,20,72,67,156,52,508,467,257,440,276,439,33,11
%N a(n) = Apex of XOR-triangle based on A346298(0..n).
%C This sequence is not a permutation of nonnegative integers, example a(1) = a(14) = 1.
%C Row 1 of the XOR-triangle is the smallest number such that there is no duplicated value in any row of this triangle.
%F a(2^n) = A346298(2^n).
%F a(2^n + m) XOR a(m) = A346298(2^p + q) XOR A346298(q) if 2^n + m = 2^p + q.
%F a(n) <> a(n + 2^m + 2^p).
%e Example for a(8):
%e Row 9: 16 ... = a(8)
%e / \
%e Row 8: 14 30 ...
%e / \ / \
%e Row 7: 4 10 20 ...
%e / \ / \ / \
%e Row 6: 5 1 11 31 ...
%e / \ / \ / \ / \
%e Row 5: 3 6 7 12 19 ...
%e / \ / \ / \ / \ / \
%e Row 4: 7 4 2 5 9 26 ...
%e / \ / \ / \ / \ / \ / \
%e Row 3: 2 5 1 3 6 15 21 ...
%e / \ / \ / \ / \ / \ / \ / \
%e Row 2: 1 3 6 7 4 2 13 24 ...
%e / \ / \ / \ / \ / \ / \ / \ / \
%e Row 1: 0 1 2 4 3 7 5 8 16 ...
%e ---------------------------------------
%e Row 1 is A346298(0), ..., A346298(8)
%e Row 2 is A346298(0) XOR A346298(1), ..., A346298(7) XOR A346298(8)
%e Row 9: a(8)
%Y Cf. A346298.
%K nonn,base
%O 0,3
%A _Thomas Scheuerle_, Jul 14 2021