A003509 a(n) is the index of the first occurrence of n in 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 M0833)

2, 3, 7, 13, 21, 31

Offset

2,1

Comments

Here, the author has chosen to use the value of the terms (k = 2, 3, 4, ...) as index, while in A005991, the index is n for the n-th distinct term (n = 1 => first value k = 2, n = 2 => second value k = 3, n = 3 => second (distinct) value k(7) = 4, ...). - 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=2..7.

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) = A005991(n-2) + 1 for n > 2. - M. F. Hasler, Nov 07 2025

Example

Sequence A155934(m = 2, 3, ...) starts (2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, ...). The first term is A155934(m = 2) = 2, therefore a(2) = 2.
The next term is A155934(m = 3) = 3, therefore a(3) = 3.
The next distinct term is A155934(m = 7) = 4, so a(4) = 7. And so on.

Crossrefs

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

Sequence in context: A325875 A049887 A048216 * A394768 A385931 A238432

Adjacent sequences: A003506 A003507 A003508 * A003510 A003511 A003512

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Title made more specific by Sean A. Irvine, Jun 04 2015

Definition improved by M. F. Hasler, Nov 06 2025

Status

approved