A386493 Minimum squared diameter of a cloud of points in the square lattice such that no three points form an isosceles triangle.

0, 1, 5, 5, 13, 17, 25, 25, 37, 41, 52, 53

Offset

1,3

Comments

The condition that there is no isosceles triangle is equivalent to: for each point, the distances to other points are all different.

Links

Table of n, a(n) for n=1..12.

Benoît Daene, Python code to compute all minimal solutions

Benoît Daene, All minimal solutions for n=1..12

digiSchool, Points acceptables (in French).

Example

a( 1)= 0, {(0, 0)}
a( 2)= 1, {(0, 0), (1, 0)}
a( 3)= 5, {(0, 0), (0, 1), (1, 2)}
a( 4)= 5, {(0, 0), (0, 1), (2, 0), (2, 1)}
a( 5)=13, {(0, 0), (0, 1), (1, 2), (1, 3), (3, 0)}
a( 6)=17, {(0, 1), (1, 0), (2, 3), (2, 4), (3, 2), (4, 2)}
a( 7)=25, {(0, 1), (0, 2), (1, 0), (1, 5), (2, 4), (3, 2), (3, 4)}
a( 8)=25, {(0, 2), (1, 1), (2, 1), (3, 0), (3, 5), (4, 3), (4, 4), (5, 2)}
a( 9)=37, {(0, 1), (0, 4), (1, 1), (1, 5), (2, 0), (3, 0), (3, 6), (4, 5), (5, 2)}
a(10)=41, {(0, 1), (0, 4), (1, 1), (2, 0), (2, 6), (3, 0), (3, 6), (4, 5), (5, 2), (5, 5)}
a(11)=52, {(0, 1), (1, 1), (2, 0), (3, 0), (3, 6), (3, 7), (5, 2), (5, 5), (5, 6), (6, 2), (7, 1)}
a(12)=53, {(0, 2), (0, 4), (1, 1), (2, 1), (2, 6), (3, 0), (5, 0), (5, 7), (6, 5), (6, 6), (7, 2), (7, 4)}

Prog

(Python) # see Links

Crossrefs

Relaxation of A193839.

Sequence in context: A147016 A146370 A164927 * A094904 A286456 A352209

Adjacent sequences: A386490 A386491 A386492 * A386494 A386495 A386496

Keyword

nonn,more,hard

Author

Benoît Daene, Aug 26 2025

Status

approved