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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).

%I A367129 #17 Dec 19 2024 11:45:36
%S A367129 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,
%T A367129 14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,21,21,21,24,24,24,
%U A367129 21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22
%N 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).
%C A367129 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.
%H A367129 Kevin Ryde, <a href="/A367129/b367129.txt">Table of n, a(n) for n = 1..10000</a>
%H A367129 Kevin Ryde, <a href="/A367128/a367128.c.txt">C Code</a>
%H A367129 Wikipedia, <a href="https://en.wikipedia.org/wiki/Distance_(graph_theory)">Distance (graph theory)</a>
%e A367129 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:
%e A367129   i    = 1  2  3  4
%e A367129   a(i) = 1, 1, 1, 2
%e A367129          1->1->1->2
%e A367129 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.
%o A367129 (C) /* See links */
%Y A367129 Cf. A367128, A365576, A364392, A362248, A360744, A360745, A360746.
%K A367129 nonn
%O A367129 1,4
%A A367129 _Neal Gersh Tolunsky_, Nov 05 2023