A363995 Rectangular array by descending antidiagonals: row n consists of the numbers k such that n = 1 + maximal runlength of 0's in the ternary representation of k.

1, 2, 3, 4, 6, 9, 5, 10, 18, 27, 7, 11, 28, 54, 81, 8, 12, 29, 82, 162, 243, 13, 15, 36, 83, 244, 486, 729, 14, 19, 45, 108, 245, 730, 1458, 2187, 16, 20, 55, 135, 324, 731, 2188, 4374, 6561, 17, 21, 56, 163, 405, 972, 2189, 6562, 13122, 19683, 22, 24, 63

Offset

1,2

Comments

Every positive integer occurs exactly once.

Links

Table of n, a(n) for n=1..58.

Example

Corner:
    1     2      4     5     7      8     13     14     16     17
    3     6     10    11    12     15     19     20     21     24
    9    18     28    29    36     45     55     56     63     72
   27    54     82    83   108    135    163    164    189    216
   81   162    244   245   324    405    487    488    567    648
  243   486    730   731   972   1215   1459   1460   1701   1944
Let r(n) = maximal runlength of 0s in the ternary representation of n, for n >=1, so that (r(n)) = (0,0,1,0,0,1,0,0,2,...). Thus, r(9)=2, so that the first term in row 3 of the array is 9.

Mathematica

d[n_] := d[n] = First[RealDigits[n, 3]]; f[w_] := FromDigits[w, 3];
s = Map[Split, Table[d[n], {n, 1, 2187}]];
x[n_] := Select[s, MemberQ[#, Table[0, n]] &];
u[n_] := Map[Flatten, x[n]];
t0 = Flatten[Table[FromDigits[#, 3] & /@ Tuples[{1, 2}, n], {n, 5}]];
t = Join[{t0}, Table[Map[f, u[n]], {n, 1, 7}]] ;
TableForm[t]  (* this sequence as an array *)
Table[t[[n - k + 1, k]], {n, 8}, {k, n, 1, -1}] // Flatten (* this sequence *)
(* Next, another program *)
nwCornerD[lists_] := Quiet[Flatten[Reap[NestWhile[# + 1 &, 1, ! {} ===
Sow[Check[lists[[# - Binomial[Floor[1/2 + Sqrt[2*#]], 2]]][[1 - # +
Binomial[Floor[3/2 + Sqrt[2*#]], 2]]], {}]] &[#] &]][[2]]]];
z = 10; radix = 3;
tmp = Map[Max[Map[Count[#, 0] &, #]] &,
   Map[Split, IntegerDigits[Range[radix^z], radix]]];
nwCornerD[Map[Flatten[Position[tmp, #]] &, Range[0, z]]]
(* Peter J. C. Moses, Aug 01 2023 *)

Crossrefs

Cf. A000244 (column 1), A032924 (row 1), A363996.

Sequence in context: A285332 A344844 A185290 * A141396 A159849 A098168

Adjacent sequences: A363992 A363993 A363994 * A363996 A363997 A363998

Keyword

nonn,tabl,base

Author

Clark Kimberling, Jul 01 2023

Status

approved