A297932 - OEIS

%I #9 Apr 05 2020 21:21:47

%S 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 48,65,64,255,14,20,35,66,96,129,128,511,21,25,40,67,130,192,257,256,

%U 1023,22,28,49,80,131,258,384,513,512,2047,23,36,56,97,160,259

%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 0'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    3    7    15    31    63   127

%e    2    5    6    10    11    13    14

%e    4    9   12    18    19    20    25

%e    8   17   24    34    35    40    49

%e   16   33   48    66    67    80    97

%e   32   65   96   130   131   160   193

%e ***

%e 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 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[0], d]], {d, 0, 8}]] (* A297932 array *)

%t u[d_] := Flatten[Position[t[0], d]]

%t v[d_, n_] := u[d][[n]];

%t Table[v[n, k - n + 1], {k, 0, 11}, {n, 0, k}] // Flatten (* A297932 sequence *)

%Y Cf. A297769, A297933.

%K nonn,base,easy,tabl

%O 1,2

%A _Clark Kimberling_, Jan 26 2018