A175488 Triangle read by rows: T(n,m) = the largest positive integer that, when written in binary, occurs as a substring both in binary m and in binary n.

1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 2, 1, 2, 5, 1, 2, 3, 2, 2, 6, 1, 1, 3, 1, 1, 3, 7, 1, 2, 1, 4, 2, 2, 1, 8, 1, 2, 1, 4, 2, 2, 1, 4, 9, 1, 2, 1, 2, 5, 2, 1, 2, 2, 10, 1, 2, 3, 2, 5, 3, 3, 2, 2, 5, 11, 1, 2, 3, 4, 2, 6, 3, 4, 4, 2, 3, 12, 1, 2, 3, 2, 5, 6, 3, 2, 2, 5, 5, 6, 13, 1, 2, 3, 2, 2, 6, 7, 2, 2, 2, 3, 6, 6, 14

Offset: 1

Author

Leroy Quet, May 28 2010

Keywords

• base
• tabl
• nonn

Examples

			Triangle begins:
  1;
  1, 2;
  1, 1, 3;
  1, 2, 1, 4;
  1, 2, 1, 2, 5;
  1, 2, 3, 2, 2, 6;
  ...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Crossrefs

Cf. A007088, A175466.

Programs

Maple

f:= proc(n,m) local s,R,i;
  for s from ilog2(m)+1 to 1 by -1 do
    R:= {seq(floor(n/2^i) mod 2^s,i=0 .. ilog2(n)+1-s)}
      intersect {seq(floor(m/2^i) mod 2^s,i=0 .. ilog2(m)+1-s)};
    if R <> {} then return max(R) fi
  od
end proc:
for n from 1 to 15 do
  seq(f(n,m),m=1..n)
od; # Robert Israel, Jan 20 2025

Formula

T(2^k * n + j, n) = n for 0 <= j < 2^k. - Robert Israel, Jan 21 2025

Extensions

Keyword:tabl added and sequences extended by R. J. Mathar, Sep 28 2010