A367128 - OEIS

%I #18 Dec 19 2024 11:45:36

%S 1,1,1,1,2,2,2,3,3,4,4,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,

%T 7,8,8,8,8,8,8,8,9,9,9,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,

%U 10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10

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

%C The radius of the sequence's digraph is the smallest 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.

%H Kevin Ryde, <a href="/A367128/b367128.txt">Table of n, a(n) for n = 1..10000</a>

%H Kevin Ryde, <a href="/A367128/a367128.c.txt">C Code</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Distance_(graph_theory)">Distance (graph theory)</a>

%e To find a(5), we can look at the eccentricity of each location:

%e   i            = 1     2     3     4

%e   a(i)         = 1,    1,    1,    1

%e                  1 <-> 1 <-> 1 <-> 1

%e   eccentricity = 3     2     2     3

%e i=1 has eccentricity 3 because it requires up to 3 jumps to reach any other location (3 to i=4), and similarly i=4 has eccentricity 3 too.

%e i=2 and i=3 have eccentricity 2 as they require at most 2 jumps to reach anywhere.

%e The smallest eccentricity of any location is 2, which makes 2 the radius of the sequence's digraph, so a(5)=2.

%o (C) /* See links */

%Y Cf. A367129, A365576, A364392, A362248, A360744, A360745, A360746.

%K nonn

%O 1,5

%A _Neal Gersh Tolunsky_, Nov 05 2023