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%I #14 Feb 28 2015 14:37:48
%S 4,6,2,3,3,3,2,3,3
%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) = smallest value of i such that EKG-i meets EKG-n after f(n) steps.
%C Does a(n) always exist?
%C See video for explanation.
%C Recommended for elementary school teachers to experiment with to teach factoring.
%H Gordon Hamilton, <a href="http://www.youtube.com/playlist?list=PLSrbLTVLJpcj3ioFnN6aTYLzLIcgg64DI">EKG Ancestral Links</a>
%e 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).
%e EKG-3: 3, 6, 2, 4, 8, 10, 5, 15, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11...
%e EKG-6: 6, 2, 4, 8, 10, 5, 15, 3, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11...
%e EKG-9: 9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11...
%e EKG-12: 12, 2, 4, 6, 3, 9, 15, 5, 10, 8, 14, 7, 21, 18, 16, 20, 22, 11...
%e EKG-5: 5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11...
%e Of these, the smallest EKG sequence is numbered 3 so a(5) = 3.
%Y A255198 records the number of closest neighbors.
%Y For examples of EKG-n, see A064413, A169841, A169837, A169843, A169855, A169849.
%Y Cf. A255583.
%K nonn,more
%O 2,1
%A _Gordon Hamilton_, Feb 24 2015
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