This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345237 #37 Aug 21 2021 16:24:54 %S A345237 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 A345237 121,39,67,105,9,108,128,160,152,132,190,210,176,105,221,157,147,208, %U A345237 151,16,99,116,225,139,25,20,72,67,156,52,508,467,257,440,276,439,33,11 %N A345237 a(n) = Apex of XOR-triangle based on A346298(0..n). %C A345237 This sequence is not a permutation of nonnegative integers, example a(1) = a(14) = 1. %C A345237 Row 1 of the XOR-triangle is the smallest number such that there is no duplicated value in any row of this triangle. %F A345237 a(2^n) = A346298(2^n). %F A345237 a(2^n + m) XOR a(m) = A346298(2^p + q) XOR A346298(q) if 2^n + m = 2^p + q. %F A345237 a(n) <> a(n + 2^m + 2^p). %e A345237 Example for a(8): %e A345237 Row 9: 16 ... = a(8) %e A345237 / \ %e A345237 Row 8: 14 30 ... %e A345237 / \ / \ %e A345237 Row 7: 4 10 20 ... %e A345237 / \ / \ / \ %e A345237 Row 6: 5 1 11 31 ... %e A345237 / \ / \ / \ / \ %e A345237 Row 5: 3 6 7 12 19 ... %e A345237 / \ / \ / \ / \ / \ %e A345237 Row 4: 7 4 2 5 9 26 ... %e A345237 / \ / \ / \ / \ / \ / \ %e A345237 Row 3: 2 5 1 3 6 15 21 ... %e A345237 / \ / \ / \ / \ / \ / \ / \ %e A345237 Row 2: 1 3 6 7 4 2 13 24 ... %e A345237 / \ / \ / \ / \ / \ / \ / \ / \ %e A345237 Row 1: 0 1 2 4 3 7 5 8 16 ... %e A345237 --------------------------------------- %e A345237 Row 1 is A346298(0), ..., A346298(8) %e A345237 Row 2 is A346298(0) XOR A346298(1), ..., A346298(7) XOR A346298(8) %e A345237 Row 9: a(8) %Y A345237 Cf. A346298. %K A345237 nonn,base %O A345237 0,3 %A A345237 _Thomas Scheuerle_, Jul 14 2021