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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.

%I A297933 #8 Apr 26 2021 19:24:06
%S A297933 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,
%T A297933 126,127,16,22,39,61,124,191,254,255,17,24,46,79,125,252,383,510,511,
%U A297933 18,25,55,94,159,253,508,767,1022,1023,20,26,56,111,190,319
%N 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.
%C A297933 Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
%e A297933 Northwest corner:
%e A297933   1      2     4     5     8     9    10    16
%e A297933   3      6    11    12    13    19    22    24
%e A297933   7     14    23    28    29    39    46    55
%e A297933   15    30    47    60    61    79    94   111
%e A297933   31    62    95   124   125   159   190   223
%e A297933   63   126   191   252   253   319   382   447
%e A297933   127  254   383   508   509   639   766   895
%e A297933 ***
%e A297933 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.
%t A297933 b = 2; s[n_] := Split[IntegerDigits[n, b]];
%t A297933 m[n_, d_] := Union[Select[s[n], MemberQ[#, d] &]]
%t A297933 h[n_, d_] := Max[Map[Length, m[n, d]]]
%t A297933 z = 6000; w = t[d_] := Table[h[n, d], {n, 1, z}] /. -Infinity -> 0
%t A297933 TableForm[Table[Flatten[Position[t[1], d]], {d, 0, 8}]]  (* A297933 array *)
%t A297933 u[d_] := Flatten[Position[t[1], d]]
%t A297933 v[d_, n_] := u[d][[n]];
%t A297933 Table[v[n, k - n + 1], {k, 1, 11}, {n, 1, k}] // Flatten (* A297933 sequence *)
%Y A297933 Cf. A297769, A297932.
%K A297933 nonn,base,easy,tabl
%O A297933 1,2
%A A297933 _Clark Kimberling_, Jan 26 2018