A376915 Minimum number of edge pieces in a rectangular jigsaw puzzle with n pieces.

1, 2, 3, 4, 5, 6, 7, 8, 8, 10, 11, 10, 13, 14, 12, 12, 17, 14, 19, 14, 16, 22, 23, 16, 16, 26, 20, 18, 29, 18, 31, 20, 24, 34, 20, 20, 37, 38, 28, 22, 41, 22, 43, 26, 24, 46, 47, 24, 24, 26, 36, 30, 53, 26, 28, 26, 40, 58, 59, 28, 61, 62, 28, 28, 32, 30, 67

Offset

1,2

Comments

Rules for the puzzle:

- the shape of the puzzle is rectangular

- the shape of the pieces is square (or rectangular, as long as they are all the same size)

- the puzzle is completely filled

How to find the sequence:

- find the factors of n

- find the lowest sum of the factors (that multiply to n)

- sum these factors, multiply by 2, subtract 4 (calculate the number of edge pieces)

Links

Table of n, a(n) for n=1..67.

Example

x (n=1, edge pieces = 1)
xxx (n=3, edge pieces = 3)
xx (n=4, edge pieces = 4)
xx
xxx (n=9, edge pieces = 8)
x.x
xxx
xxxxx (n=10, edge pieces = 10)
xxxxx
xxxxxxxxxxx (n=11, edge pieces = 11)
xxxxxxx (n=14, edge pieces = 14)
xxxxxxx
xxxxxxxxxxxxxxxxxxx (n=19, edge pieces = 19)
xxxxx (n=20, edge pieces = 14)
x...x
x...x
xxxxx

Prog

(PARI) a(n)={fordiv(n, d, if(d<n && n/d<=d, return(2*(n/d+d-2)))); n} \\ Andrew Howroyd, Oct 12 2024

Crossrefs

Sequence in context: A291572 A265541 A128557 * A265542 A103303 A297232

Adjacent sequences: A376912 A376913 A376914 * A376916 A376917 A376918

Keyword

nonn

Author

Arnout Nell, Oct 09 2024

Status

approved