A005991 - OEIS

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A005991

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 last term in each string of equal entries in the {k(m)} sequence (see A155934).
(Formerly M1582)

2, 6, 12, 20, 30, 43 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	REFERENCES	`Problem E2429, Amer. Math. Monthly, 81 (1974), 1112-1113.` `N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).`
	LINKS	`Table of n, a(n) for n=1..6.` `Index entries for sequences related to binary matrices`
	EXAMPLE	`Since k(2) = 2 then a(1) = 2` `Since k(3) = k(4) = k(5) = k(6) = 3 then a(2) = 6` `Since k(7) = k(8) = ... = k(12) = 4 then a(3) = 12` `Since k(13) = k(14) = ... = k(20) = 5 then a(4) = 20` `Since k(21) = k(22) = ... = k(30) = 6 then a(5) = 30` `Since k(31) = k(32) = ... = k(43) = 7 then a(6) = 43`
	CROSSREFS	`Cf. A155934.` `Sequence in context: A160929 A103505 A002378 * A194110 A184432 A003274` `Adjacent sequences: A005988 A005989 A005990 * A005992 A005993 A005994`
	KEYWORD	`nonn,more`
	AUTHOR	`N. J. A. Sloane.`
	EXTENSIONS	`Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008`
	STATUS	`approved`

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Last modified May 26 02:46 EDT 2013. Contains 225653 sequences.