A005991 a(n) is the index of the last occurrence of the n-th distinct term (equal to n+1) in sequence A155934(m) = k(m) = 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. (Formerly M1582)

2, 6, 12, 20, 30, 43

Offset

1,1

Comments

While this sequence uses indices n = 1, 2, 3,... to refer to the n-th distinct term of A155934 (which is equal to n+1), sequence A003509 uses indices n = 2, 3, 4, ... to refer to the values of the distinct terms. - M. F. Hasler, Nov 07 2025

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 + 2) - 1, for n >= 1. - Sean A. Irvine, Jun 04 2015, corrected by M. F. Hasler, Nov 07 2025

Example

Since k(2) = 2, we have a(1) = 2.
Since k(3) = k(4) = k(5) = k(6) = 3, we have a(2) = 6.
Since k(7) = k(8) = ... = k(12) = 4, we have a(3) = 12.
Since k(13) = k(14) = ... = k(20) = 5, we have a(4) = 20.
Since k(21) = k(22) = ... = k(30) = 6, we have a(5) = 30.
Since k(31) = k(32) = ... = k(43) = 7, we have a(6) = 43.

Crossrefs

Cf. A003509 (index of first term), A155934.

Sequence in context: A279019 A002378 A349704 * 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

Better definition from M. F. Hasler, Nov 06 2025

Status

approved