A339731 - OEIS

A339731

Let G be the undirected graph with nodes {g_k, k > 0} such that for any k > 0, g_k is connected to g_{k+1} and g_{A064413(k)} is connected to g_{A064413(k+1)}; a(n) is the distance between g_1 and g_n.

%I #15 Dec 18 2020 04:46:35

%S 0,1,2,2,3,3,4,4,3,4,5,4,5,5,4,5,6,5,6,6,5,6,7,6,7,6,7,7,8,8,8,7,6,7,

%T 8,7,8,7,6,7,8,8,9,8,8,8,9,9,9,8,7,8,9,9,9,8,7,8,9,10,10,9,10,10,10,

%U 10,10,9,8,9,10,10,10,9,10,11,11,11,11,10,10

%N Let G be the undirected graph with nodes {g_k, k > 0} such that for any k > 0, g_k is connected to g_{k+1} and g_{A064413(k)} is connected to g_{A064413(k+1)}; a(n) is the distance between g_1 and g_n.

%H Rémy Sigrist, <a href="/A339731/b339731.txt">Table of n, a(n) for n = 1..10000</a>

%H Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, <a href="https://arxiv.org/abs/2012.04625">Finding structure in sequences of real numbers via graph theory: a problem list</a>, arXiv:2012.04625, Dec 08, 2020.

%H Rémy Sigrist, <a href="/A339731/a339731.png">Illustration of initial terms</a>

%H Rémy Sigrist, <a href="/A339731/a339731.gp.txt">PARI program for A339731</a>

%F abs(a(n) - a(k)) <= abs(n-k) for any n, k > 0.

%F a(n) = A339733(n, 1).

%o (PARI) See Links section.

%Y See A339695 for a similar sequence.

%Y Cf. A064413, A064664, A339732, A339733.

%K nonn

%O 1,3

%A _Rémy Sigrist_, Dec 14 2020