A255524 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) = smallest value of i such that EKG-i meets EKG-n after f(n) steps.

4, 6, 2, 3, 3, 3, 2, 3, 3

Offset: 2

Author

Gordon Hamilton, Feb 24 2015

Keywords

• nonn
• more

Comments

Does a(n) always exist?

See video for explanation.

Recommended for elementary school teachers to experiment with to teach factoring.

Examples

			a(5) = 3 because the EKG sequence starting with 5 (EKG-5) 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...
EKG-6:  6, 2, 4, 8, 10, 5, 15, 3, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11...
EKG-9:  9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11...
EKG-12: 12, 2, 4, 6, 3, 9, 15, 5, 10, 8, 14, 7, 21, 18, 16, 20, 22, 11...
EKG-5:  5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11...
Of these, the smallest EKG sequence is numbered 3 so a(5) = 3.
		

Links

• Gordon Hamilton, EKG Ancestral Links

Crossrefs

A255198 records the number of closest neighbors.

For examples of EKG-n, see A064413, A169841, A169837, A169843, A169855, A169849.

Cf. A255583.