A360364 - OEIS

%I #14 Feb 06 2023 15:04:57

%S 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 44,48,49,50,51,52,56,60,32,16,65,66,67,68,72,76,80,96,112,84,87,86,

%U 81,93,89,69,117,101,21,107,104,105,110,98,102,122,74,90,42,63

%N 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 All terms are distinct.

%C Every positive integer appears in this sequence:

%C - each time a power of 2 appears in A360363, say A360363(n) = 2^k,

%C - 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 - then A360363(n+1) = 2^k + v and T(n,n) = v.

%H Rémy Sigrist, <a href="/A360364/b360364.txt">Table of n, a(n) for n = 1..7021</a>

%H Rémy Sigrist, <a href="/A360364/a360364.png">Scatterplot of (n, T(n, k)) for n = 1..1227, k = 1..n</a>

%H 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 Rémy Sigrist, <a href="/A360364/a360364.txt">C++ program</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e Table begins:

%e     3,

%e     2, 1,

%e     5, 6, 7,

%e     9, 10, 11, 12,

%e     13, 14, 15, 8, 4,

%e     17, 18, 19, 20, 24, 28,

%e     33, 34, 35, 36, 40, 44, 48,

%e     49, 50, 51, 52, 56, 60, 32, 16,

%e     65, 66, 67, 68, 72, 76, 80, 96, 112,

%e     84, 87, 86, 81, 93, 89, 69, 117, 101, 21,

%e     107, 104, 105, 110, 98, 102, 122, 74, 90, 42, 63,

%e     129, 130, 131, 132, 136, 140, 144, 160, 176, 192, 213, 234,

%e     151, 148, 149, 146, 158, 154, 134, 182, 166, 214, 195, 252, 22,

%e     ...

%o (C++) See Links section.

%Y Cf. A360363.

%K nonn,base,look,tabl

%O 1,1

%A _Rémy Sigrist_, Feb 04 2023