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A297769
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.
3
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, 64, 127, 170, 13, 24, 47, 65, 126, 128, 255, 341, 18, 28, 48, 95, 129, 254, 256, 511, 682, 19, 29, 60, 96, 191, 257, 510, 512, 1023, 1365, 20, 34, 61, 124, 192
OFFSET
1,2
COMMENTS
Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
EXAMPLE
Northwest corner:
1 2 5 10 21 42 85
3 4 6 9 11 12 13
7 8 14 17 23 24 28
15 16 30 33 47 48 60
31 32 62 65 95 96 124
63 64 126 129 191 192 252
***
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.
MATHEMATICA
b = 2; u[n_] := Max[Map[Length, Split[IntegerDigits[n, b]]]];
z = 4096; r[n_] := Select[Range[z], u[#] == n &]
TableForm[Table[r[n], {n, 1, 12}]] (* A297769, array *)
v[n_, k_] := r[k][[n]];
Table[v[k, n - k + 1], {n, 11}, {k, n, 1, -1}] // Flatten (* A297769, sequence *)
CROSSREFS
KEYWORD
nonn,base,easy,tabl
AUTHOR
Clark Kimberling, Apr 10 2018
STATUS
approved