%I A005991 M1582
%S A005991 2,6,12,20,30,43
%N A005991 Let k(n) denote the least integer such that every n X n (0,1)-matrix 
               with exactly k(n) ones in each row and in each column contains a 
               2 X 2 submatrix without zeros. The sequence gives the index n of 
               the last term in each string of equal entries in k(n).
%C A005991 1 is not in the sequence because a 1 X 1 matrix does not contain a 2 
               X 2 submatrix. - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 
               2008
%D A005991 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005991 Problem E2429, Amer. Math. Monthly, 81 (1974), 1112-1113.
%H A005991 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%e A005991 Since k(2) = 2 then a(1) = 2
%e A005991 Since k(3) = k(4) = k(5) = k(6) = 3 then a(2) = 6
%e A005991 Since k(7) = k(8) = ... = k(12) = 4 then a(3) = 12
%e A005991 Since k(13) = k(14) = ... = k(20) = 5 then a(4) = 20
%e A005991 Since k(21) = k(22) = ... = k(30) = 6 then a(5) = 30
%e A005991 Since k(31) = k(32) = ... = k(43) = 7 then a(6) = 43
%Y A005991 Sequence in context: A160929 A103505 A002378 this_sequence A003274 A121315 
               A078878
%Y A005991 Adjacent sequences: A005988 A005989 A005990 this_sequence A005992 A005993 
               A005994
%K A005991 nonn,more
%O A005991 1,1
%A A005991 N. J. A. Sloane (njas(AT)research.att.com).
%E A005991 Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008