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