A339695 - OEIS

A339695

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_{A006068(k)} is connected to g_{A006068(k+1)}; a(n) is the distance between g_0 and g_n.

%I #14 Dec 18 2020 04:46:21

%S 0,1,2,2,3,4,4,3,4,5,6,6,6,5,6,5,6,7,8,8,9,10,10,9,9,8,7,8,9,9,8,7,8,

%T 9,10,10,11,12,12,11,12,13,14,14,14,13,14,13,13,12,12,11,10,9,10,11,

%U 12,13,14,14,13,13,12,11,12,13,14,14,15,16,16,15,16

%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_{A006068(k)} is connected to g_{A006068(k+1)}; a(n) is the distance between g_0 and g_n.

%H Rémy Sigrist, <a href="/A339695/b339695.txt">Table of n, a(n) for n = 0..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="/A339695/a339695.png">Illustration of initial terms</a>

%H Rémy Sigrist, <a href="/A339695/a339695.gp.txt">PARI program for A339695</a>

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

%F a(n) = A339697(n, 0).

%o (PARI) See Links section.

%Y See A339731 for a similar sequence.

%Y Cf. A003188, A006068, A339696, A339697.

%K nonn

%O 0,3

%A _Rémy Sigrist_, Dec 13 2020