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.

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

Table of n, a(n) for n=1..105.

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))

Rémy Sigrist, PARI program for A339733

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

Cf. A064413, A064664, A339732, A339732.

Sequence in context: A061895 A129678 A261773 * A226207 A226324 A339697

Adjacent sequences: A339730 A339731 A339732 * A339734 A339735 A339736

Keyword

nonn,tabl

Author

Rémy Sigrist, Dec 14 2020

Status

approved