A297932 -id:A297932 - cp's OEIS frontend

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

Clark Kimberling, Apr 10 2018

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

			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.

Index entries for sequences that are permutations of the natural numbers

Cf. A007088, A297932, A297933.

Rows: A000975, A037969, A037970, A037971.

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 *)

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.

Original entry on oeis.org

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

Clark Kimberling, Jan 26 2018

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

			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.

Cf. A297769, A297932.

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 *)

cp's OEIS Frontend

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.

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