A060655 Pack n integer-sided rectangles into the smallest possible square so that no sides of the rectangle are the same. Sequence gives the side of the smallest square.

2, 4, 6, 8, 11, 14, 18, 21, 24, 28, 32, 37, 41, 46, 51, 55, 60

Offset

1,1

Comments

Those terms that are > ceiling(sqrt(n*(n+1)*(2n+1)/3)) are only the best currently known solutions. - Larry Reeves (larryr(AT)acm.org), Apr 19 2001

a(1)-a(17) except a(15) are known to be the smallest possible. - Sean A. Irvine, Dec 13 2022

Links

Table of n, a(n) for n=1..17.

E. J. Friedman, Math. Magic: August 1999, Question #2

Sean A. Irvine, Java program (github)

Sean A. Irvine, Solution for a(16)

Sean A. Irvine, Solution for a(17)

Formula

a(n) >= sqrt(n*(n+1)*(2n+1)/3).

Crossrefs

Sequence in context: A212555 A328787 A339573 * A117490 A359275 A032514

Adjacent sequences: A060652 A060653 A060654 * A060656 A060657 A060658

Keyword

nonn,hard,more

Author

Jason Earls, Apr 18 2001

Extensions

Data updated from values at Friedman link by Sean A. Irvine, Dec 05 2022

a(16) from Sean A. Irvine, Dec 13 2022

a(17) from Sean A. Irvine, Dec 17 2022

Status

approved