A255524 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

Does a(n) always exist?

See video for explanation.

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

LINKS

Table of n, a(n) for n=2..10.

Gordon Hamilton, EKG Ancestral Links

EXAMPLE

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.

CROSSREFS

A255198 records the number of closest neighbors.

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

Cf. A255583.

Sequence in context: A195860 A106143 A359283 * A077158 A059854 A155991

Adjacent sequences: A255521 A255522 A255523 * A255525 A255526 A255527

KEYWORD

nonn,more

AUTHOR

Gordon Hamilton, Feb 24 2015

STATUS

approved