cp's OEIS Frontend

A161000 Triangle read by rows: For 1 <= m <= n, t(n,m) = the smallest positive integer that when read in binary contains exactly (n+1-m) runs of 0's and 1's, all runs being of distinct lengths m through n in any order within binary t(n,m).

%I A161000 #7 Mar 11 2014 01:32:31
%S A161000 1,4,3,35,24,7,536,391,112,15,16775,12400,3599,480,31,1060976,790031,
%T A161000 229856,30751,1984,63,135007759,100893152,29390879,3934144,254015,
%U A161000 8064,127,34460631520,25799194655,7520126912,1006886975,65019776,2064511
%N A161000 Triangle read by rows: For 1 <= m <= n, t(n,m) = the smallest positive integer that when read in binary contains exactly (n+1-m) runs of 0's and 1's, all runs being of distinct lengths m through n in any order within binary t(n,m).
%C A161000 Think of binary n as a string S of 0's and 1's. By a "run" of 0's or 1's, it is meant either a substring all of contiguous 0's, each run bounded by 1's or the edge of S; or a substring all of contiguous 1's, each run bounded by 0's or the edge of S.
%e A161000 The terms of the first few rows of the triangle converted to binary:
%e A161000 1
%e A161000 100, 11
%e A161000 100011, 11000, 111
%e A161000 1000011000, 110000111, 1110000, 1111
%e A161000 Note that all terms in row n have a run with n 0s or 1's (and no run of more 0's or 1s), and all terms in column m have a run of m 0's or 1's (but no run of fewer 0's or 1's). Each length of run occurs exactly once in each binary number.
%Y A161000 Cf. A161001.
%K A161000 base,nonn,tabl
%O A161000 1,2
%A A161000 _Leroy Quet_, Jun 01 2009
%E A161000 Extended by _Ray Chandler_, Jun 13 2009