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%I #19 Oct 06 2018 15:25:30
%S 3,9,3,14,9,20,8,10,17,36,11,37,21,12,17,57,13,51,12,21,39,62,23,38,
%T 39,25,27,82,23,90,31,39,49,30,31,101,66,39,27,116,31,129,41,39,66,
%U 135,41,65,46,45,45,148,46,67,57,45,83,168,53,178,91,69,64,64,53
%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). Then a(n) = number of steps for this to happen.
%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.
%H Rémy Sigrist, <a href="/A255583/b255583.txt">Table of n, a(n) for n = 2..2000</a>
%H Gordon Hamilton, <a href="https://www.youtube.com/watch?v=yd2jr30K2R4">The EKG Sequence and the Tree of Numbers</a>, Oct 2013.
%H Rémy Sigrist, <a href="/A255583/a255583.gp.txt">PARI program for A255583</a>
%e a(5) = 14 because the EKG sequence starting with 5 (EKG-5, A169841) merges 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)
%o (PARI) See Links section.
%Y Cf. A064413, A169837, A169841, A169843, A169849, A169857.
%Y A255524 gives the smallest closest neighbor.
%K nonn
%O 2,1
%A _Gordon Hamilton_, Feb 26 2015
%E More terms from _Rémy Sigrist_, Oct 06 2018
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