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

1,2

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.

Example

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.

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 *)

Crossrefs

Cf. A297769, A297932.

Sequence in context: A048201 A186004 A056534 * A360646 A130264 A072659

Adjacent sequences: A297930 A297931 A297932 * A297934 A297935 A297936

Keyword

nonn,base,easy,tabl

Author

Clark Kimberling, Jan 26 2018

Status

approved