A339731 -id:A339731 - cp's OEIS frontend

A339695 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)}; a(n) is the distance between g_0 and g_n.

0, 1, 2, 2, 3, 4, 4, 3, 4, 5, 6, 6, 6, 5, 6, 5, 6, 7, 8, 8, 9, 10, 10, 9, 9, 8, 7, 8, 9, 9, 8, 7, 8, 9, 10, 10, 11, 12, 12, 11, 12, 13, 14, 14, 14, 13, 14, 13, 13, 12, 12, 11, 10, 9, 10, 11, 12, 13, 14, 14, 13, 13, 12, 11, 12, 13, 14, 14, 15, 16, 16, 15, 16

Offset: 0

Rémy Sigrist, Dec 13 2020

nonn

Rémy Sigrist, Table of n, a(n) for n = 0..10000
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, Illustration of initial terms
Rémy Sigrist, PARI program for A339695

See A339731 for a similar sequence.

Cf. A003188, A006068, A339696, A339697.

PARI
```
See Links section.
```

abs(a(n) - a(k)) <= abs(n-k) for any n, k >= 0.

a(n) = A339697(n, 0).

A339732 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)}; a(n) is the number of nodes at distance n from g_1.

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 8, 11, 15, 17, 28, 39, 48, 64, 94, 116, 164, 217, 289, 395, 542, 729, 919, 1154, 1598, 2091, 2747, 3702, 4867, 6338, 8290, 10873, 14533, 18919, 24577, 31918, 41857

Offset: 0

Rémy Sigrist, Dec 14 2020

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 A339732

Cf. A064413, A064664, A339731, A339733.

PARI
```
See Links section.
```

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.

Original entry on oeis.org

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

Rémy Sigrist, Dec 14 2020

			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

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

Cf. A064413, A064664, A339732, A339732.

PARI
```
See Links section.
```

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).

cp's OEIS Frontend

A339695 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)}; a(n) is the distance between g_0 and g_n.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A339732 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)}; a(n) is the number of nodes at distance n from g_1.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula