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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.
3

%I #15 Jan 23 2025 00:21:52

%S 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,

%T 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,

%U 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

%N 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.

%H Robert Israel, <a href="/A175488/b175488.txt">Table of n, a(n) for n = 1..10011</a> (first 141 rows, flattened)

%F T(2^k * n + j, n) = n for 0 <= j < 2^k. - _Robert Israel_, Jan 21 2025

%e Triangle begins:

%e 1;

%e 1, 2;

%e 1, 1, 3;

%e 1, 2, 1, 4;

%e 1, 2, 1, 2, 5;

%e 1, 2, 3, 2, 2, 6;

%e ...

%p f:= proc(n,m) local s,R,i;

%p for s from ilog2(m)+1 to 1 by -1 do

%p R:= {seq(floor(n/2^i) mod 2^s,i=0 .. ilog2(n)+1-s)}

%p intersect {seq(floor(m/2^i) mod 2^s,i=0 .. ilog2(m)+1-s)};

%p if R <> {} then return max(R) fi

%p od

%p end proc:

%p for n from 1 to 15 do

%p seq(f(n,m),m=1..n)

%p od; # _Robert Israel_, Jan 20 2025

%Y Cf. A007088, A175466.

%K base,tabl,nonn,changed

%O 1,3

%A _Leroy Quet_, May 28 2010

%E Keyword:tabl added and sequences extended by _R. J. Mathar_, Sep 28 2010