A389940 Numbers k for which a sphere of radius k is a member of at least 1 set of 4 spheres of coprime positive integer radii which are tangent to a plane when arranged as mutually tangent to one another.

1, 3, 4, 7, 12, 19, 21, 27, 28, 36, 37, 39, 48, 52, 57, 61, 63, 75, 76, 84, 91, 93, 108, 111, 112, 117, 124, 127, 129, 144, 147, 156, 169, 172, 175, 189, 192, 196, 208, 217, 219, 228, 243, 247, 252, 259, 271, 273, 279, 291, 300, 325, 331, 336, 351, 363, 364

Offset

1,2

Comments

Unique values of A390148.

It is observed that most terms occur in multiple examples, e.g., 3 is a member of {1, 3, 3, 3}, {3, 3, 7, 21}, and {3, 4, 12, 12}. The first few that do not are 1: {1, 3, 3, 3}, 4: {3, 4, 12, 12}, and 36: {28, 36, 63, 252}.

It is unknown if specific terms can otherwise be found algorithmically, though it is conjectured that the general increase in gap size between successive terms as n increases continues to infinity.

Links

Table of n, a(n) for n=1..57.

Example

3, 4, and 12 are all in the sequence because spheres of radius 3, 4, 12, and 12 are tangent to a plane when arranged as mutually tangent to one another.

Crossrefs

Cf. A390148.

Sequence in context: A362222 A310007 A158237 * A117950 A025047 A050342

Adjacent sequences: A389937 A389938 A389939 * A389941 A389942 A389943

Keyword

nonn

Author

Charles L. Hohn, Oct 19 2025

Status

approved