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

1,2

Comments

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

Links

Table of n, a(n) for n=1..61.

Index entries for sequences that are permutations of the natural numbers

Example

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.

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 *)

Crossrefs

Cf. A007088, A297932, A297933.

Rows: A000975, A037969, A037970, A037971.

Sequence in context: A119474 A308098 A029654 * A213921 A335422 A214870

Adjacent sequences: A297766 A297767 A297768 * A297770 A297771 A297772

Keyword

nonn,base,easy,tabl

Author

Clark Kimberling, Apr 10 2018

Status

approved