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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 28 17:31 EDT 2022. Contains 354907 sequences. (Running on oeis4.)