%I #13 Aug 31 2023 15:50:52

%S 0,1,3,2,5,6,4,7,10,12,8,9,11,13,14,15,17,18,20,24,31,16,19,22,21,25,

%T 47,23,26,27,30,28,29,63,48,58,32,33,34,36,40,79,49,59,35,37,39,38,44,

%U 41,95,50,62,42,45,43,51,46,52,56,111,53,90,54,55,107

%N Triangle T(n, k), n >= 0, k = 0..n-1, read by rows and filled the greedy way with distinct nonnegative integers such that the powers of 2 in the binary expansion of T(k, 0) also appear in that of T(n, k).

%C As a flat sequence, this is a permutation of the nonnegative integers (as each row starts with the least value not yet in the sequence); see A365233 for the inverse.

%H Rémy Sigrist, <a href="/A365232/b365232.txt">Table of n, a(n) for n = 0..10010</a> (rows for n = 0..140 flattened)

%H Rémy Sigrist, <a href="/A365232/a365232.gp.txt">PARI program</a>

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

%e Triangle T(n, k) begins:

%e 0;

%e 1, 3;

%e 2, 5, 6;

%e 4, 7, 10, 12;

%e 8, 9, 11, 13, 14;

%e 15, 17, 18, 20, 24, 31;

%e 16, 19, 22, 21, 25, 47, 23;

%e 26, 27, 30, 28, 29, 63, 48, 58;

%e 32, 33, 34, 36, 40, 79, 49, 59, 35;

%e 37, 39, 38, 44, 41, 95, 50, 62, 42, 45;

%e .......................................

%e T(k, 0) 0 1 2 4 8 15 16 26 32 37

%o (PARI) See Links section.

%Y See A365230 for a similar sequence.

%Y Cf. A365233 (inverse).

%K nonn,base,look,tabl

%O 0,3

%A _Rémy Sigrist_, Aug 27 2023