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

1,1

Comments

Every positive integer occurs exactly once.

Links

Table of n, a(n) for n=1..59.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A136764 A136765 A011041 * A291836 A100831 A136763

Adjacent sequences: A363993 A363994 A363995 * A363997 A363998 A363999

Keyword

nonn,tabl,base

Author

Clark Kimberling, Jul 01 2023

Status

approved