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%I #54 Feb 28 2015 14:39:12
%S 1,1,1,4,1,6,2,2,5
%N 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) = number of i such that EKG-i meets EKG-n after f(n) steps.
%C This sequence can be used in a classroom to introduce students to divisors.
%C For an explanatory video, see the Youtube link.
%C 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
%C 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.
%C EKG-3 and EKG-5 (below) do not merge at step 3, because the sequences are not identical from that point forward.
%H Gordon Hamilton, <a href="http://youtu.be/yd2jr30K2R4">The EKG Sequence and the Tree of Numbers</a>, Oct 2013.
%e 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).
%e EKG-3: 3, 6, 2, 4, 8, 10, 5, 15, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169837)
%e EKG-6: 6, 2, 4, 8, 10, 5, 15, 3, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169843)
%e EKG-9: 9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169849)
%e EKG-12: 12, 2, 4, 6, 3, 9, 15, 5, 10, 8, 14, 7, 21, 18, 16, 20, 22, 11, ... (A169855)
%e EKG-5: 5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11, ... (A169841)
%e 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).
%Y Cf. A064413, A169837, A169841, A169843, A169849, A169857, A255583.
%Y A255524 gives the smallest closest neighbor.
%K nonn,more
%O 2,4
%A _Gordon Hamilton_, Feb 16 2015
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