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).

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, 47, 23, 26, 27, 30, 28, 29, 63, 48, 58, 32, 33, 34, 36, 40, 79, 49, 59, 35, 37, 39, 38, 44, 41, 95, 50, 62, 42, 45, 43, 51, 46, 52, 56, 111, 53, 90, 54, 55, 107

Offset: 0

Author

Rémy Sigrist, Aug 27 2023

Keywords

• nonn
• base
• look
• tabl

Comments

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.

Examples

			Triangle T(n, k) begins:
          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, 47, 23;
         26, 27, 30, 28, 29, 63, 48, 58;
         32, 33, 34, 36, 40, 79, 49, 59, 35;
         37, 39, 38, 44, 41, 95, 50, 62, 42, 45;
         .......................................
T(k, 0)   0   1   2   4   8  15  16  26  32  37
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10010 (rows for n = 0..140 flattened)
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A365230 for a similar sequence.

Cf. A365233 (inverse).

Programs

PARI

See Links section.