A169855 -id:A169855 - cp's OEIS frontend

A255583 Let EKG-n denote the EKG sequence (A064413) started with n rather than 2, and suppose EKG-n first merges with some other EKG-i (i >= 2). Then a(n) = number of steps for this to happen.

3, 9, 3, 14, 9, 20, 8, 10, 17, 36, 11, 37, 21, 12, 17, 57, 13, 51, 12, 21, 39, 62, 23, 38, 39, 25, 27, 82, 23, 90, 31, 39, 49, 30, 31, 101, 66, 39, 27, 116, 31, 129, 41, 39, 66, 135, 41, 65, 46, 45, 45, 148, 46, 67, 57, 45, 83, 168, 53, 178, 91, 69, 64, 64, 53

Offset: 2

Gordon Hamilton, Feb 26 2015

nonn

Merging means that the sequences are identical for all future steps. EKG-2 and EKG-5 merge at step 44. From then on the sequences are identical.

			a(5) = 14 because the EKG sequence starting with 5 (EKG-5, A169841) merges with sequences EKG-3, EKG-6, EKG-9 and EKG-12 simultaneously when all sequences hit 18.
EKG-3:  3, 6, 2, 4, 8, 10, 5, 15, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169837)
EKG-6:  6, 2, 4, 8, 10, 5, 15, 3, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169843)
EKG-9:  9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169849)
EKG-12: 12, 2, 4, 6, 3, 9, 15, 5, 10, 8, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169855)
EKG-5:  5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11, ... (A169841)

Rémy Sigrist, Table of n, a(n) for n = 2..2000
Gordon Hamilton, The EKG Sequence and the Tree of Numbers, Oct 2013.
Rémy Sigrist, PARI program for A255583

Cf. A064413, A169837, A169841, A169843, A169849, A169857.

A255524 gives the smallest closest neighbor.

PARI
```
\\ See Links section.
```

More terms from Rémy Sigrist, Oct 06 2018

A255198 Let EKG-n denote the EKG sequence (A064413) started with n rather than 2, and suppose EKG-n first merges with some other EKG-i (i >= 2) sequence after f(n) (= A255583(n)) steps; then a(n) = number of i such that EKG-i meets EKG-n after f(n) steps.

Original entry on oeis.org

1, 1, 1, 4, 1, 6, 2, 2, 5

Offset: 2

Gordon Hamilton, Feb 16 2015

This sequence can be used in a classroom to introduce students to divisors.
For an explanatory video, see the Youtube link.
EKG-5 merges with EKG-2 after three steps, so some care is needed in the definition. Perhaps the offset should be 3 rather than 2? - N. J. A. Sloane, Feb 24 2015
Merging means that the sequences are identical for all future steps.  EKG-2 and EKG-5 merge at step 44.  From then on the sequences are identical.
EKG-3 and EKG-5 (below) do not merge at step 3, because the sequences are not identical from that point forward.

			a(5) = 4 because the EKG sequence starting with 5 (EKG-5, A169841) starts coinciding with sequences EKG-3, EKG-6, EKG-9 and EKG-12 simultaneously (when all sequences hit 18).
EKG-3:  3, 6, 2, 4, 8, 10, 5, 15, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169837)
EKG-6:  6, 2, 4, 8, 10, 5, 15, 3, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169843)
EKG-9:  9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169849)
EKG-12: 12, 2, 4, 6, 3, 9, 15, 5, 10, 8, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169855)
EKG-5:  5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11, ... (A169841)
a(12) = 3 because the EKG sequence starting with 12 (EKG-12, A169855) starts coinciding with sequences EKG-3, EKG-6, and EKG-9 simultaneously (when all sequences hit 14).

Gordon Hamilton, The EKG Sequence and the Tree of Numbers, Oct 2013.

Cf. A064413, A169837, A169841, A169843, A169849, A169857, A255583.

A255524 gives the smallest closest neighbor.

cp's OEIS Frontend

A255583 Let EKG-n denote the EKG sequence (A064413) started with n rather than 2, and suppose EKG-n first merges with some other EKG-i (i >= 2). Then a(n) = number of steps for this to happen.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions