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

1,3

Links

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

Formula

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

Example

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

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

Crossrefs

Cf. A007088, A175466.

Sequence in context: A324668 A128221 A327856 * A309914 A364911 A115758

Adjacent sequences: A175485 A175486 A175487 * A175489 A175490 A175491

Keyword

base,tabl,nonn

Author

Leroy Quet, May 28 2010

Extensions

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

Status

approved