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A339733
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.
3
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, 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, 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
OFFSET
1,4
LINKS
Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625, Dec 08, 2020.
Rémy Sigrist, Colored representation of the table for 1 <= x, y <= 1000 (where the hue is function of T(x, y))
FORMULA
T(n, n) = 0.
T(n, k) = T(k, n).
T(n, k) <= abs(n-k).
T(m, k) <= T(m, n) + T(n, k).
T(n, 1) = A339731(n).
EXAMPLE
Array T(n, k) begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12
---+---------------------------------------
1| 0 1 2 2 3 3 4 4 3 4 5 4
2| 1 0 1 1 2 2 3 3 2 3 4 3
3| 2 1 0 1 2 1 2 2 1 2 3 2
4| 2 1 1 0 1 1 2 3 2 2 3 3
5| 3 2 2 1 0 1 2 2 2 1 2 3
6| 3 2 1 1 1 0 1 2 2 2 3 3
7| 4 3 2 2 2 1 0 1 2 2 3 2
8| 4 3 2 3 2 2 1 0 1 1 2 1
9| 3 2 1 2 2 2 2 1 0 1 2 1
10| 4 3 2 2 1 2 2 1 1 0 1 2
11| 5 4 3 3 2 3 3 2 2 1 0 1
12| 4 3 2 3 3 3 2 1 1 2 1 0
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Dec 14 2020
STATUS
approved