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

0,3

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.

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A365230 for a similar sequence.

Cf. A365233 (inverse).

Sequence in context: A303768 A182801 A026098 * A135764 A253551 A265895

Adjacent sequences: A365229 A365230 A365231 * A365233 A365234 A365235

Keyword

nonn,base,look,tabl

Author

Rémy Sigrist, Aug 27 2023

Status

approved