cp's OEIS Frontend

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.

%I A363995 #12 Aug 02 2023 11:48:54
%S A363995 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,
%T A363995 244,486,729,14,19,45,108,245,730,1458,2187,16,20,55,135,324,731,2188,
%U A363995 4374,6561,17,21,56,163,405,972,2189,6562,13122,19683,22,24,63
%N 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.
%C A363995 Every positive integer occurs exactly once.
%e A363995 Corner:
%e A363995     1     2      4     5     7      8     13     14     16     17
%e A363995     3     6     10    11    12     15     19     20     21     24
%e A363995     9    18     28    29    36     45     55     56     63     72
%e A363995    27    54     82    83   108    135    163    164    189    216
%e A363995    81   162    244   245   324    405    487    488    567    648
%e A363995   243   486    730   731   972   1215   1459   1460   1701   1944
%e A363995 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.
%t A363995 d[n_] := d[n] = First[RealDigits[n, 3]]; f[w_] := FromDigits[w, 3];
%t A363995 s = Map[Split, Table[d[n], {n, 1, 2187}]];
%t A363995 x[n_] := Select[s, MemberQ[#, Table[0, n]] &];
%t A363995 u[n_] := Map[Flatten, x[n]];
%t A363995 t0 = Flatten[Table[FromDigits[#, 3] & /@ Tuples[{1, 2}, n], {n, 5}]];
%t A363995 t = Join[{t0}, Table[Map[f, u[n]], {n, 1, 7}]] ;
%t A363995 TableForm[t]  (* this sequence as an array *)
%t A363995 Table[t[[n - k + 1, k]], {n, 8}, {k, n, 1, -1}] // Flatten (* this sequence *)
%t A363995 (* Next, another program *)
%t A363995 nwCornerD[lists_] := Quiet[Flatten[Reap[NestWhile[# + 1 &, 1, ! {} ===
%t A363995 Sow[Check[lists[[# - Binomial[Floor[1/2 + Sqrt[2*#]], 2]]][[1 - # +
%t A363995 Binomial[Floor[3/2 + Sqrt[2*#]], 2]]], {}]] &[#] &]][[2]]]];
%t A363995 z = 10; radix = 3;
%t A363995 tmp = Map[Max[Map[Count[#, 0] &, #]] &,
%t A363995    Map[Split, IntegerDigits[Range[radix^z], radix]]];
%t A363995 nwCornerD[Map[Flatten[Position[tmp, #]] &, Range[0, z]]]
%t A363995 (* _Peter J. C. Moses_, Aug 01 2023 *)
%Y A363995 Cf. A000244 (column 1), A032924 (row 1), A363996.
%K A363995 nonn,tabl,base
%O A363995 1,2
%A A363995 _Clark Kimberling_, Jul 01 2023