A297933 - OEIS

%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