A297769 Rectangular array read by antidiagonals: row n gives the numbers whose base-2 digits d(m), d(m-1), ..., d(0) have maximal run-length n.

1, 2, 3, 5, 4, 7, 10, 6, 8, 15, 21, 9, 14, 16, 31, 42, 11, 17, 30, 32, 63, 85, 12, 23, 33, 62, 64, 127, 170, 13, 24, 47, 65, 126, 128, 255, 341, 18, 28, 48, 95, 129, 254, 256, 511, 682, 19, 29, 60, 96, 191, 257, 510, 512, 1023, 1365, 20, 34, 61, 124, 192

Offset: 1

Author

Clark Kimberling, Apr 10 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    5    10    21    42     85
   3    4    6     9    11    12     13
   7    8   14    17    23    24     28
  15   16   30    33    47    48     60
  31   32   62    65    95    96    124
  63   64  126   129   191   192    252
***
Base-2 digits of 23: 1,0,1,1,1, with run 1,1,1, of maximal length 3, so that 23 is in row 3.
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A007088, A297932, A297933.

Rows: A000975, A037969, A037970, A037971.

Programs

Mathematica

b = 2; u[n_] := Max[Map[Length, Split[IntegerDigits[n, b]]]];
z = 4096; r[n_] := Select[Range[z], u[#] == n &]
TableForm[Table[r[n], {n, 1, 12}]]  (* A297769, array *)
v[n_, k_] := r[k][[n]];
Table[v[k, n - k + 1], {n, 11}, {k, n, 1, -1}] // Flatten (* A297769, sequence *)