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

Author

Gordon Hamilton, Feb 26 2015

Keywords

• nonn

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.

Examples

			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)
		

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

Crossrefs

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

A255524 gives the smallest closest neighbor.

Programs

PARI

\\ See Links section.

Extensions

More terms from Rémy Sigrist, Oct 06 2018