

A255198


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


1




OFFSET

2,4


COMMENTS

This sequence can be used in a classroom to introduce students to divisors.
For an explanatory video, see the Youtube link.
EKG5 merges with EKG2 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. EKG2 and EKG5 merge at step 44. From then on the sequences are identical.
EKG3 and EKG5 (below) do not merge at step 3, because the sequences are not identical from that point forward.


LINKS



EXAMPLE

a(5) = 4 because the EKG sequence starting with 5 (EKG5, A169841) starts coinciding with sequences EKG3, EKG6, EKG9 and EKG12 simultaneously (when all sequences hit 18).
EKG3: 3, 6, 2, 4, 8, 10, 5, 15, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169837)
EKG6: 6, 2, 4, 8, 10, 5, 15, 3, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169843)
EKG9: 9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169849)
EKG12: 12, 2, 4, 6, 3, 9, 15, 5, 10, 8, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169855)
EKG5: 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 (EKG12, A169855) starts coinciding with sequences EKG3, EKG6, and EKG9 simultaneously (when all sequences hit 14).


CROSSREFS

A255524 gives the smallest closest neighbor.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



