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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.

%I A297932 #9 Apr 05 2020 21:21:47
%S A297932 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,
%T A297932 48,65,64,255,14,20,35,66,96,129,128,511,21,25,40,67,130,192,257,256,
%U A297932 1023,22,28,49,80,131,258,384,513,512,2047,23,36,56,97,160,259
%N 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.
%C A297932 Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
%e A297932 Northwest corner:
%e A297932    1    3    7    15    31    63   127
%e A297932    2    5    6    10    11    13    14
%e A297932    4    9   12    18    19    20    25
%e A297932    8   17   24    34    35    40    49
%e A297932   16   33   48    66    67    80    97
%e A297932   32   65   96   130   131   160   193
%e A297932 ***
%e A297932 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.
%t A297932 b = 2; s[n_] := Split[IntegerDigits[n, b]];
%t A297932 m[n_, d_] := Union[Select[s[n], MemberQ[#, d] &]]
%t A297932 h[n_, d_] := Max[Map[Length, m[n, d]]]
%t A297932 z = 6000; w = t[d_] := Table[h[n, d], {n, 1, z}] /. -Infinity -> 0
%t A297932 TableForm[Table[Flatten[Position[t[0], d]], {d, 0, 8}]] (* A297932 array *)
%t A297932 u[d_] := Flatten[Position[t[0], d]]
%t A297932 v[d_, n_] := u[d][[n]];
%t A297932 Table[v[n, k - n + 1], {k, 0, 11}, {n, 0, k}] // Flatten (* A297932 sequence *)
%Y A297932 Cf. A297769, A297933.
%K A297932 nonn,base,easy,tabl
%O A297932 1,2
%A A297932 _Clark Kimberling_, Jan 26 2018