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