cp's OEIS Frontend

A370893 Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation has exactly n runs.

%I A370893 #10 Mar 15 2024 05:12:01
%S A370893 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,
%T A370893 96,275,820,80,14,20,46,97,276,821,2460,121,17,21,47,100,277,825,2462,
%U A370893 7381,242,18,23,48,101,289,826,2463,7382,22143
%N A370893 Rectangular array, read by antidiagonals: row n consists of the numbers m whose ternary representation has exactly n runs.
%C A370893 Every positive integer occurs exactly once.
%e A370893 Corner:
%e A370893      1     2     4     8    13    26    40
%e A370893      3     5     6     7     9    12    14
%e A370893     10    11    15    16    19    20    21
%e A370893     30    32    33    34    46    47    48
%e A370893     91    92    96    97   100   101   102
%e A370893    273   275   276   277   289   290   291
%e A370893    820   821   825   826   829   830   831
%e A370893   2460  2462  2463  2464  2476  2477  2478
%e A370893 The ternary representation of 12 is 110, which has 2 runs: 11 and 0.
%t A370893 a[n_] := a[n] = Select[Range[25000], Length[Split[IntegerDigits[#, 3]]] == n &];
%t A370893 t[n_, k_] := a[n][[k]];
%t A370893 Grid[Table[t[n, k], {n, 1, 10}, {k, 1, 10}]] (* array *)
%t A370893 Table[t[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* sequence *)
%Y A370893 Cf. A007089, A043555 (number of runs).
%Y A370893 Cf. A370698 (binary), A370924, A370925.
%K A370893 nonn,base,tabl
%O A370893 1,2
%A A370893 _Clark Kimberling_, Mar 13 2024