A383020 G(n) is a graph constructed with nodes labelled with integers n through n+a(n). Edges are drawn between consecutive integers and between integers sharing the same largest prime factor. a(n) is the smallest integer for which G(n) is not planar.

8, 7, 10, 10, 12, 11, 12, 12, 11, 14, 13, 12, 11, 13, 12, 11, 10, 14, 13, 15, 17, 16, 15, 17, 16, 15, 16, 19, 18, 18, 17, 16, 16, 15, 14, 17, 16, 15, 15, 14, 13, 13, 12, 15, 19, 18, 17, 16, 18, 19, 20, 22, 21, 22, 21, 23, 23, 22, 21, 24, 23, 22, 24, 23, 24, 23

Offset: 2

Author

Gordon Hamilton, Apr 20 2025

Keywords

• nonn

Examples

			a(2) = 8: the graph G(2) has nodes labelled 2-10. Consecutive integers are connected by an edge. Also pairwise connected are: 3, 6, and 9 because they have 3 as the largest prime factor; 2, 4, and 8 because they have 2 as the largest prime factor; 5 and 10 because they have 5 as the largest prime factor. Nodes 2 and 10 are not connected because although 2 is a prime factor of 10, it is not the largest prime factor. This graph is non-planar. a(2) is larger than 7 because the nodes 2-9 make a planar graph. So a(2) = 8.
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A006530.

Formula

a(n) >= a(n-1) - 1. - Pontus von Brömssen, Apr 22 2025

Extensions

a(15) corrected and a(41)-a(67) added by Pontus von Brömssen, Apr 21 2025