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A370893
Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation has exactly n runs.
3
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.
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
KEYWORD
nonn,base,tabl
AUTHOR
Clark Kimberling, Mar 13 2024
STATUS
approved