A370893 Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation has exactly n runs.

1, 2, 3, 4, 5, 10, 8, 6, 11, 30, 13, 7, 15, 32, 91, 26, 9, 16, 33, 92, 273, 40, 12, 19, 34, 96, 275, 820, 80, 14, 20, 46, 97, 276, 821, 2460, 121, 17, 21, 47, 100, 277, 825, 2462, 7381, 242, 18, 23, 48, 101, 289, 826, 2463, 7382, 22143

Offset: 1

Author

Clark Kimberling, Mar 13 2024

Keywords

• nonn
• base
• tabl

Comments

Every positive integer occurs exactly once.

Examples

			Corner:
     1     2     4     8    13    26    40
     3     5     6     7     9    12    14
    10    11    15    16    19    20    21
    30    32    33    34    46    47    48
    91    92    96    97   100   101   102
   273   275   276   277   289   290   291
   820   821   825   826   829   830   831
  2460  2462  2463  2464  2476  2477  2478
The ternary representation of 12 is 110, which has 2 runs: 11 and 0.
		

Crossrefs

Cf. A007089, A043555 (number of runs).

Cf. A370698 (binary), A370924, A370925.

Programs

Mathematica

a[n_] := a[n] = Select[Range[25000], Length[Split[IntegerDigits[#, 3]]] == n &];
t[n_, k_] := a[n][[k]];
Grid[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]] (* array *)
Table[t[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* sequence *)