A297932 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 0's.

1, 3, 2, 7, 5, 4, 15, 6, 9, 8, 31, 10, 12, 17, 16, 63, 11, 18, 24, 33, 32, 127, 13, 19, 34, 48, 65, 64, 255, 14, 20, 35, 66, 96, 129, 128, 511, 21, 25, 40, 67, 130, 192, 257, 256, 1023, 22, 28, 49, 80, 131, 258, 384, 513, 512, 2047, 23, 36, 56, 97, 160, 259

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    3    7    15    31    63   127
   2    5    6    10    11    13    14
   4    9   12    18    19    20    25
   8   17   24    34    35    40    49
  16   33   48    66    67    80    97
  32   65   96   130   131   160   193
***
Base-2 digits of 72: 1,0,0,1,0,0,0 with runs 00 and 000 of 0's, so that 72 is in row 3.
		

Crossrefs

Cf. A297769, A297933.

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[0], d]], {d, 0, 8}]] (* A297932 array *)
u[d_] := Flatten[Position[t[0], d]]
v[d_, n_] := u[d][[n]];
Table[v[n, k - n + 1], {k, 0, 11}, {n, 0, k}] // Flatten (* A297932 sequence *)