

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




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), 11121113.
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



