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.
EKG-5 merges with EKG-2 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. EKG-2 and EKG-5 merge at step 44. From then on the sequences are identical.
EKG-3 and EKG-5 (below) do not merge at step 3, because the sequences are not identical from that point forward.
LINKS
Gordon Hamilton, The EKG Sequence and the Tree of Numbers, Oct 2013.
EXAMPLE
a(5) = 4 because the EKG sequence starting with 5 (EKG-5, A169841) 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, ... (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)
a(12) = 3 because the EKG sequence starting with 12 (EKG-12, A169855) starts coinciding with sequences EKG-3, EKG-6, and EKG-9 simultaneously (when all sequences hit 14).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gordon Hamilton, Feb 16 2015
STATUS
approved