A363996 Rectangular array by descending antidiagonals: row n consists of the numbers k such that n = 1 + maximal runlength of 1's in the ternary representation of k.

2, 6, 1, 8, 3, 4, 18, 5, 12, 13, 20, 7, 14, 39, 40, 24, 9, 22, 41, 120, 121, 26, 10, 31, 67, 122, 363, 364, 54, 11, 36, 94, 202, 365, 1092, 1093, 56, 15, 37, 117, 283, 607, 1094, 3279, 3280, 60, 16, 38, 118, 360, 850, 1822, 3281, 9840, 9841, 62, 17, 42, 119

Offset: 1

Author

Clark Kimberling, Jul 01 2023

Keywords

• nonn
• tabl
• base

Comments

Every positive integer occurs exactly once.

Examples

			Corner:
    2     6     8    18    20    24     26
    1     3     5     7     9    10     11
    4    12    14    22    31    36     37
   13    39    41    67    94   117    118
   40   120   122   202   283   360    361
  121   363   365   607   850   1089  1090
Let r(n) = maximal runlength of 1's in the ternary representation of n, for n >= 1, so that (r(n)) = (1,0,1,2,1,0,1,0,1,...). Thus, r(4)=2, so the first term in row 3 of the array is 4.
		

Crossrefs

Cf. A000244 (column 1), A032924 (row 1), A363995.

Programs

Mathematica

d[n_] := d[n] = First[RealDigits[n, 3]]; f[w_] := FromDigits[w, 3];
s = Map[Split, Table[d[n], {n, 1, 50000}]];
x[n_] := Select[s, MemberQ[#, Table[1, n]] &];
u[n_] := Map[Flatten, x[n]];
t0 = Select[Range[1, 4000], DigitCount[#, 3, 1] == 0 &, 20];
v = Table[Take[Map[f, u[n]], Min[{20, Length[u[n]]}]], {n, 1, 11}]
t = Join[{t0}, v]
TableForm[t]  (* this sequence as an array *)
Table[t[[n - k + 1, k]], {n, 11}, {k, n, 1, -1}] // Flatten (* this sequence *)