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%I #5 Dec 18 2020 04:04:08
%S 0,1,1,2,0,2,2,1,1,2,3,1,0,1,3,3,2,1,1,2,3,4,2,2,0,2,2,4,4,3,1,1,1,1,
%T 3,4,3,3,2,1,0,1,2,3,3,4,2,2,2,1,1,2,2,2,4,5,3,1,3,2,0,2,3,1,3,5,4,4,
%U 2,2,2,1,1,2,2,2,4,4,5,3,3,2,2,2,0,2,2,2,3,3,5,5,4,2,3,1,2,1,1,2,1,3,2,4,5
%N Square array T(n, k) read by antidiagonals, n > 0 and k > 0; 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)}; T(n, k) is the distance between g_n and g_k.
%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="/A339733/a339733.png">Colored representation of the table for 1 <= x, y <= 1000</a> (where the hue is function of T(x, y))
%H Rémy Sigrist, <a href="/A339733/a339733.gp.txt">PARI program for A339733</a>
%F T(n, n) = 0.
%F T(n, k) = T(k, n).
%F T(n, k) <= abs(n-k).
%F T(m, k) <= T(m, n) + T(n, k).
%F T(n, 1) = A339731(n).
%e Array T(n, k) begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12
%e ---+---------------------------------------
%e 1| 0 1 2 2 3 3 4 4 3 4 5 4
%e 2| 1 0 1 1 2 2 3 3 2 3 4 3
%e 3| 2 1 0 1 2 1 2 2 1 2 3 2
%e 4| 2 1 1 0 1 1 2 3 2 2 3 3
%e 5| 3 2 2 1 0 1 2 2 2 1 2 3
%e 6| 3 2 1 1 1 0 1 2 2 2 3 3
%e 7| 4 3 2 2 2 1 0 1 2 2 3 2
%e 8| 4 3 2 3 2 2 1 0 1 1 2 1
%e 9| 3 2 1 2 2 2 2 1 0 1 2 1
%e 10| 4 3 2 2 1 2 2 1 1 0 1 2
%e 11| 5 4 3 3 2 3 3 2 2 1 0 1
%e 12| 4 3 2 3 3 3 2 1 1 2 1 0
%o (PARI) See Links section.
%Y Cf. A064413, A064664, A339732, A339732.
%K nonn,tabl
%O 1,4
%A _Rémy Sigrist_, Dec 14 2020
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