A367129 a(1)=a(2)=1; thereafter a(n) is the diameter of the sequence's digraph, where jumps from location i to i+-a(i) are permitted (within 1..n-1).

1, 1, 1, 2, 3, 3, 4, 4, 4, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 24, 24, 24, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22

Offset: 1

Author

Neal Gersh Tolunsky, Nov 05 2023

Keywords

• nonn

Comments

The diameter of the sequence's digraph is the largest eccentricity of any vertex (location) in the graph. The eccentricity of a location i means the largest number of jumps in the shortest path from location i to any other location.

Examples

			a(5)=3 because i=1 has the largest eccentricity of any location. i=1 takes 3 jumps to reach i=4 in the shortest path:
  i    = 1  2  3  4
  a(i) = 1, 1, 1, 2
         1->1->1->2
Every other location has eccentricity 2, which makes 3 the largest eccentricity and thus the diameter of the sequence's digraph, so a(5)=3.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10000
• Kevin Ryde, C Code
• Wikipedia, Distance (graph theory)

Crossrefs

Cf. A367128, A365576, A364392, A362248, A360744, A360745, A360746.

Programs

C

/* See links */