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

2,1

Comments

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.

Links

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

Example

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)

Prog

(PARI) \\ See Links section.

Crossrefs

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

A255524 gives the smallest closest neighbor.

Sequence in context: A170862 A083996 A010259 * A339882 A120429 A101431

Adjacent sequences: A255580 A255581 A255582 * A255584 A255585 A255586

Keyword

nonn

Author

Gordon Hamilton, Feb 26 2015

Extensions

More terms from Rémy Sigrist, Oct 06 2018

Status

approved