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A360364 Triangle T(n, k), n > 0, k = 1..n, read by rows; T(n, k) = A360363(n+1) XOR A360363(k) (where XOR denotes the bitwise XOR operator).

%I A360364 #14 Feb 06 2023 15:04:57
%S A360364 3,2,1,5,6,7,9,10,11,12,13,14,15,8,4,17,18,19,20,24,28,33,34,35,36,40,
%T A360364 44,48,49,50,51,52,56,60,32,16,65,66,67,68,72,76,80,96,112,84,87,86,
%U A360364 81,93,89,69,117,101,21,107,104,105,110,98,102,122,74,90,42,63
%N A360364 Triangle T(n, k), n > 0, k = 1..n, read by rows; T(n, k) = A360363(n+1) XOR A360363(k) (where XOR denotes the bitwise XOR operator).
%C A360364 All terms are distinct.
%C A360364 Every positive integer appears in this sequence:
%C A360364 - each time a power of 2 appears in A360363, say A360363(n) = 2^k,
%C A360364 - if the least value v missing from the bitwise XOR of two distinct terms among the first n terms of A360363 satisfies v < 2^k,
%C A360364 - then A360363(n+1) = 2^k + v and T(n,n) = v.
%H A360364 Rémy Sigrist, <a href="/A360364/b360364.txt">Table of n, a(n) for n = 1..7021</a>
%H A360364 Rémy Sigrist, <a href="/A360364/a360364.png">Scatterplot of (n, T(n, k)) for n = 1..1227, k = 1..n</a>
%H A360364 Rémy Sigrist, <a href="/A360364/a360364_1.png">Colored representation of the first 1227 rows</a> (where the hue is function of T(n, k))
%H A360364 Rémy Sigrist, <a href="/A360364/a360364.txt">C++ program</a>
%H A360364 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A360364 Table begins:
%e A360364     3,
%e A360364     2, 1,
%e A360364     5, 6, 7,
%e A360364     9, 10, 11, 12,
%e A360364     13, 14, 15, 8, 4,
%e A360364     17, 18, 19, 20, 24, 28,
%e A360364     33, 34, 35, 36, 40, 44, 48,
%e A360364     49, 50, 51, 52, 56, 60, 32, 16,
%e A360364     65, 66, 67, 68, 72, 76, 80, 96, 112,
%e A360364     84, 87, 86, 81, 93, 89, 69, 117, 101, 21,
%e A360364     107, 104, 105, 110, 98, 102, 122, 74, 90, 42, 63,
%e A360364     129, 130, 131, 132, 136, 140, 144, 160, 176, 192, 213, 234,
%e A360364     151, 148, 149, 146, 158, 154, 134, 182, 166, 214, 195, 252, 22,
%e A360364     ...
%o A360364 (C++) See Links section.
%Y A360364 Cf. A360363.
%K A360364 nonn,base,look,tabl
%O A360364 1,1
%A A360364 _Rémy Sigrist_, Feb 04 2023