A370924 Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation starts with 1 and has exactly n runs.

1, 4, 3, 13, 5, 10, 40, 9, 11, 30, 121, 12, 15, 32, 91, 364, 14, 16, 33, 92, 273, 1093, 17, 28, 34, 96, 275, 820, 3280, 27, 29, 46, 97, 276, 821, 2460, 9841, 36, 31, 47, 100, 277, 825, 2462, 7381, 29524, 39, 35, 48, 101, 289, 826, 2463, 7382, 22143

Offset: 1

Author

Clark Kimberling, Mar 13 2024

Keywords

• nonn
• base
• tabl

Comments

Every positive integer occurs in this array or A370925.

Examples

			Corner:
    1    4   13   40  121  364  1093  3280
    3    5    9   12   14   17    27    36
   10   11   15   16   28   29    31    35
   30   32   33   34   46   47    48    50
   91   92   96   97  100  101   102   104
  273  275  276  277  289  290   291   293
  820  821  825  826  829  830   831   833
		

Crossrefs

Cf. A007089, A043555, A132141, A370893, A370925.

Programs

Mathematica

d[n_] := First[IntegerDigits[n, 3]];
a[n_] := a[n] = Select[Range[30000],
d[#] == 1 && 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 *)