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

1,2

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..62.

Example

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.

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 *)

Crossrefs

Cf. A297769, A297933.

Sequence in context: A278503 A283940 A163255 * A066884 A171429 A191448

Adjacent sequences: A297929 A297930 A297931 * A297933 A297934 A297935

Keyword

nonn,base,easy,tabl

Author

Clark Kimberling, Jan 26 2018

Status

approved