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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.

%I A297769 #15 Jul 03 2021 11:21:22
%S A297769 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,
%T A297769 64,127,170,13,24,47,65,126,128,255,341,18,28,48,95,129,254,256,511,
%U A297769 682,19,29,60,96,191,257,510,512,1023,1365,20,34,61,124,192
%N 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.
%C A297769 Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
%H A297769 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A297769 Northwest corner:
%e A297769    1    2    5    10    21    42     85
%e A297769    3    4    6     9    11    12     13
%e A297769    7    8   14    17    23    24     28
%e A297769   15   16   30    33    47    48     60
%e A297769   31   32   62    65    95    96    124
%e A297769   63   64  126   129   191   192    252
%e A297769 ***
%e A297769 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.
%t A297769 b = 2; u[n_] := Max[Map[Length, Split[IntegerDigits[n, b]]]];
%t A297769 z = 4096; r[n_] := Select[Range[z], u[#] == n &]
%t A297769 TableForm[Table[r[n], {n, 1, 12}]]  (* A297769, array *)
%t A297769 v[n_, k_] := r[k][[n]];
%t A297769 Table[v[k, n - k + 1], {n, 11}, {k, n, 1, -1}] // Flatten (* A297769, sequence *)
%Y A297769 Cf. A007088, A297932, A297933.
%Y A297769 Rows: A000975, A037969, A037970, A037971.
%K A297769 nonn,base,easy,tabl
%O A297769 1,2
%A A297769 _Clark Kimberling_, Apr 10 2018