A370924 -id:A370924 - cp's OEIS frontend

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

Clark Kimberling, Mar 13 2024

Every positive integer occurs exactly once.

			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.

Cf. A007089, A043555 (number of runs).

Cf. A370698 (binary), A370924, A370925.

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 *)

A370925 Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation starts with 2 and has exactly n runs.

Original entry on oeis.org

2, 8, 6, 26, 7, 19, 80, 18, 20, 57, 242, 22, 21, 59, 172, 728, 24, 23, 60, 173, 516, 2186, 25, 55, 61, 177, 518, 1549, 6560, 54, 56, 64, 178, 519, 1550, 4647, 19682, 67, 58, 65, 181, 520, 1554, 4649, 13942

Offset: 1

Clark Kimberling, Mar 13 2024

Every positive integer occurs in this array or A370924.

			Corner:
       2     8    26    80   242   728  2186
       6     7    18    22    24    25    54
      19    20    21    23    55    56    58
      57    59    60    61    64    65    69
     172   173   177   178   181   182   183
     516   518   519   520   532   533   534
    1549  1550  1554  1555  1558  1559  1560

Cf. A007089, A157671, A370893, A370924.

d[n_] := First[IntegerDigits[n, 3]];
a[n_] := a[n] = Select[Range[30000],
d[#] == 2 && 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 *)

cp's OEIS Frontend

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

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