A255198 - OEIS

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A255198

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.

1, 1, 1, 4, 1, 6, 2, 2, 5 (list; graph; refs; listen; history; text; internal format)

	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	`Table of n, a(n) for n=2..10.` `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	`Cf. A064413, A169837, A169841, A169843, A169849, A169857, A255583.` `A255524 gives the smallest closest neighbor.` `Sequence in context: A032050 A109915 A334467 * A202521 A247362 A098987` `Adjacent sequences: A255195 A255196 A255197 * A255199 A255200 A255201`
	KEYWORD	`nonn,more`
	AUTHOR	`Gordon Hamilton, Feb 16 2015`
	STATUS	`approved`

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Last modified March 20 14:14 EDT 2023. Contains 361384 sequences. (Running on oeis4.)