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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).
(Formerly M0833)
2

%I M0833 #22 Oct 21 2023 23:30:10

%S 2,3,7,13,21,31

%N 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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H 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 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>

%Y Cf. A005991 (index of last term), A155934.

%K nonn,more

%O 2,1

%A _N. J. A. Sloane_

%E Title made more specific by _Sean A. Irvine_, Jun 04 2015