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

1,2

Comments

Every positive integer occurs exactly once.

Links

Table of n, a(n) for n=1..55.

Example

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.

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 *)

Crossrefs

Cf. A007089, A043555 (number of runs).

Cf. A370698 (binary), A370924, A370925.

Sequence in context: A348249 A161657 A338749 * A072701 A261039 A266117

Adjacent sequences: A370890 A370891 A370892 * A370894 A370895 A370896

Keyword

nonn,base,tabl

Author

Clark Kimberling, Mar 13 2024

Status

approved