A175466 Table read by antidiagonals: a(m,n) = the largest positive integer occurring, when written in binary, as a substring in both binary m and binary n.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 3, 2, 2, 3, 1, 1, 1, 2, 3, 2, 5, 2, 3, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 4, 1, 6, 1, 4, 1, 2, 1, 1, 2, 1, 4, 2, 3, 3, 2, 4, 1, 2, 1, 1, 2, 3, 2, 2, 2, 7, 2, 2

Offset: 1

Author

Leroy Quet, May 24 2010

Keywords

• base
• nonn
• tabl

Examples

			From _Rémy Sigrist_, Jul 20 2019: (Start)
Table a(n, k) begins (in decimal):
  n\k|  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
  ---+---------------------------------------------------
    1|  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1
    2|  1  2  1  2  2  2  1  2  2   2   2   2   2   2   1
    3|  1  1  3  1  1  3  3  1  1   1   3   3   3   3   3
    4|  1  2  1  4  2  2  1  4  4   2   2   4   2   2   1
    5|  1  2  1  2  5  2  1  2  2   5   5   2   5   2   1
    6|  1  2  3  2  2  6  3  2  2   2   3   6   6   6   3
    7|  1  1  3  1  1  3  7  1  1   1   3   3   3   7   7
    8|  1  2  1  4  2  2  1  8  4   2   2   4   2   2   1
    9|  1  2  1  4  2  2  1  4  9   2   2   4   2   2   1
   10|  1  2  1  2  5  2  1  2  2  10   5   2   5   2   1
   11|  1  2  3  2  5  3  3  2  2   5  11   3   5   3   3
   12|  1  2  3  4  2  6  3  4  4   2   3  12   6   6   3
   13|  1  2  3  2  5  6  3  2  2   5   5   6  13   6   3
   14|  1  2  3  2  2  6  7  2  2   2   3   6   6  14   7
   15|  1  1  3  1  1  3  7  1  1   1   3   3   3   7  15
Table a(n, k) begins (in binary):
   n\k| 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111
  ----+----------------------------------------------------------------
     1| 1  1  1   1   1   1   1    1    1    1    1    1    1    1    1
    10| 1 10  1  10  10  10   1   10   10   10   10   10   10   10    1
    11| 1  1 11   1   1  11  11    1    1    1   11   11   11   11   11
   100| 1 10  1 100  10  10   1  100  100   10   10  100   10   10    1
   101| 1 10  1  10 101  10   1   10   10  101  101   10  101   10    1
   110| 1 10 11  10  10 110  11   10   10   10   11  110  110  110   11
   111| 1  1 11   1   1  11 111    1    1    1   11   11   11  111  111
  1000| 1 10  1 100  10  10   1 1000  100   10   10  100   10   10    1
  1001| 1 10  1 100  10  10   1  100 1001   10   10  100   10   10    1
  1010| 1 10  1  10 101  10   1   10   10 1010  101   10  101   10    1
  1011| 1 10 11  10 101  11  11   10   10  101 1011   11  101   11   11
  1100| 1 10 11 100  10 110  11  100  100   10   11 1100  110  110   11
  1101| 1 10 11  10 101 110  11   10   10  101  101  110 1101  110   11
  1110| 1 10 11  10  10 110 111   10   10   10   11  110  110 1110  111
  1111| 1  1 11   1   1  11 111    1    1    1   11   11   11  111 1111
(End)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..11325
• Rémy Sigrist, Colored representation of the table for n = 1..1023 and k = 1023

Crossrefs

Cf. A043529, A004780, A175488.

Programs

PARI

sub(n) = { my (b=binary(n), s=[]); for (i=1, #b, if (b[i], for (j=i, #b, s=setunion(s, Set(fromdigits(b[i..j], 2)))))); return (s) }
T(n,k) = my (i=setintersect(sub(n), sub(k))); i[#i] \\ Rémy Sigrist, Jul 20 2019

Formula

From Rémy Sigrist, Jul 20 2019: (Start)

1 <= a(n, k) <= min(n, k).

a(n, k) = a(k, n).

a(n, n) = n.

a(n, 1) = 1.

a(n, 2) = A043529(n).

a(n, 3) = 3 iff n belongs to A004780. (End)

Extensions

More terms from Rémy Sigrist, Jul 20 2019