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

0,4

Links

Table of n, a(n) for n=0..90.

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))

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).

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A003188, A006068, A339695, A339696.

Sequence in context: A339733 A226207 A226324 * A023604 A219660 A060964

Adjacent sequences: A339694 A339695 A339696 * A339698 A339699 A339700

Keyword

nonn,tabl

Author

Rémy Sigrist, Dec 13 2020

Status

approved