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A365232 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).

%I A365232 #13 Aug 31 2023 15:50:52
%S A365232 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 A365232 47,23,26,27,30,28,29,63,48,58,32,33,34,36,40,79,49,59,35,37,39,38,44,
%U A365232 41,95,50,62,42,45,43,51,46,52,56,111,53,90,54,55,107
%N A365232 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 A365232 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 A365232 Rémy Sigrist, <a href="/A365232/b365232.txt">Table of n, a(n) for n = 0..10010</a> (rows for n = 0..140 flattened)
%H A365232 Rémy Sigrist, <a href="/A365232/a365232.gp.txt">PARI program</a>
%H A365232 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A365232 Triangle T(n, k) begins:
%e A365232           0;
%e A365232           1,  3;
%e A365232           2,  5,  6;
%e A365232           4,  7, 10, 12;
%e A365232           8,  9, 11, 13, 14;
%e A365232          15, 17, 18, 20, 24, 31;
%e A365232          16, 19, 22, 21, 25, 47, 23;
%e A365232          26, 27, 30, 28, 29, 63, 48, 58;
%e A365232          32, 33, 34, 36, 40, 79, 49, 59, 35;
%e A365232          37, 39, 38, 44, 41, 95, 50, 62, 42, 45;
%e A365232          .......................................
%e A365232 T(k, 0)   0   1   2   4   8  15  16  26  32  37
%o A365232 (PARI) See Links section.
%Y A365232 See A365230 for a similar sequence.
%Y A365232 Cf. A365233 (inverse).
%K A365232 nonn,base,look,tabl
%O A365232 0,3
%A A365232 _Rémy Sigrist_, Aug 27 2023