A339697 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_{A006068(k)} is connected to g_{A006068(k+1)}; T(n, k) is the distance between g_n and g_k.
0, 1, 1, 2, 0, 2, 2, 1, 1, 2, 3, 1, 0, 1, 3, 4, 2, 1, 1, 2, 4, 4, 3, 2, 0, 2, 3, 4, 3, 3, 3, 1, 1, 3, 3, 3, 4, 2, 2, 2, 0, 2, 2, 2, 4, 5, 3, 1, 2, 1, 1, 2, 1, 3, 5, 6, 4, 2, 2, 1, 0, 1, 2, 2, 4, 6, 6, 5, 3, 3, 2, 1, 1, 2, 3, 3, 5, 6, 6, 5, 4, 4, 3, 2, 0, 2, 3, 4, 4, 5, 6
Offset: 0
Examples
Array T(n, k) begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12
---+------------------------------------------
0| 0 1 2 2 3 4 4 3 4 5 6 6 6
1| 1 0 1 1 2 3 3 2 3 4 5 5 5
2| 2 1 0 1 2 3 2 1 2 3 4 4 4
3| 2 1 1 0 1 2 2 2 3 4 5 5 5
4| 3 2 2 1 0 1 1 2 3 4 5 5 4
5| 4 3 3 2 1 0 1 2 3 4 5 4 3
6| 4 3 2 2 1 1 0 1 2 3 4 4 4
7| 3 2 1 2 2 2 1 0 1 2 3 3 3
8| 4 3 2 3 3 3 2 1 0 1 2 2 2
9| 5 4 3 4 4 4 3 2 1 0 1 1 2
10| 6 5 4 5 5 5 4 3 2 1 0 1 2
11| 6 5 4 5 5 4 4 3 2 1 1 0 1
12| 6 5 4 5 4 3 4 3 2 2 2 1 0
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, PARI program for A339697
- Rémy Sigrist, Colored representation of the table for 0 <= x, y <= 2^10 (where the hue is function of T(x, y))
Programs
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PARI
See Links section.
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, 0) = A339695(n).