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

1,1

REFERENCES

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.

E. T. Wang and R. K. Guy, Problem E2429, Amer. Math. Monthly, 81 (1974), 1112-1113.

Index entries for sequences related to binary matrices

FORMULA

a(n) = A003509(n + 1) - 1. - Sean A. Irvine, Jun 04 2015

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. A003509 (index of first term), A155934.

Sequence in context: A103505 A279019 A002378 * A266194 A194110 A291876

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 February 19 12:48 EST 2018. Contains 299333 sequences. (Running on oeis4.)