A297933 Rectangular array, by antidiagonals: Row n gives the numbers whose base-2 digits d(m), d(m-1), ..., d(0) having n as maximal run-length of 1's.

1, 2, 3, 4, 6, 7, 5, 11, 14, 15, 8, 12, 23, 30, 31, 9, 13, 28, 47, 62, 63, 10, 19, 29, 60, 95, 126, 127, 16, 22, 39, 61, 124, 191, 254, 255, 17, 24, 46, 79, 125, 252, 383, 510, 511, 18, 25, 55, 94, 159, 253, 508, 767, 1022, 1023, 20, 26, 56, 111, 190, 319

Offset: 1

Author

Clark Kimberling, Jan 26 2018

Keywords

• nonn
• base
• easy
• tabl

Comments

Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.

Examples

			Northwest corner:
  1      2     4     5     8     9    10    16
  3      6    11    12    13    19    22    24
  7     14    23    28    29    39    46    55
  15    30    47    60    61    79    94   111
  31    62    95   124   125   159   190   223
  63   126   191   252   253   319   382   447
  127  254   383   508   509   639   766   895
***
Base-2 digits of 59: 1,1,1,0,1,1 with runs 111 and 11 of 1's, so that 59 is in row 3.
		

Crossrefs

Cf. A297769, A297932.

Programs

Mathematica

b = 2; s[n_] := Split[IntegerDigits[n, b]];
m[n_, d_] := Union[Select[s[n], MemberQ[#, d] &]]
h[n_, d_] := Max[Map[Length, m[n, d]]]
z = 6000; w = t[d_] := Table[h[n, d], {n, 1, z}] /. -Infinity -> 0
TableForm[Table[Flatten[Position[t[1], d]], {d, 0, 8}]]  (* A297933 array *)
u[d_] := Flatten[Position[t[1], d]]
v[d_, n_] := u[d][[n]];
Table[v[n, k - n + 1], {k, 1, 11}, {n, 1, k}] // Flatten (* A297933 sequence *)