cp's OEIS Frontend

A003509 Let k(m) denote the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros. The sequence gives the index n of the first term in each string of equal entries in the {k(m)} sequence (see A155934).

%I A003509 M0833 #22 Oct 21 2023 23:30:10
%S A003509 2,3,7,13,21,31
%N A003509 Let k(m) denote the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros. The sequence gives the index n of the first term in each string of equal entries in the {k(m)} sequence (see A155934).
%D A003509 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003509 E. T. Wang and R. K. Guy, <a href="http://www.jstor.org/stable/2319052">Problem E2429</a>, Amer. Math. Monthly, 81 (1974), 1112-1113.
%H A003509 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%Y A003509 Cf. A005991 (index of last term), A155934.
%K A003509 nonn,more
%O A003509 2,1
%A A003509 _N. J. A. Sloane_
%E A003509 Title made more specific by _Sean A. Irvine_, Jun 04 2015