cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A255524 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.

Original entry on oeis.org

4, 6, 2, 3, 3, 3, 2, 3, 3
Offset: 2

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Author

Gordon Hamilton, Feb 24 2015

Keywords

Comments

Does a(n) always exist?
See video for explanation.
Recommended for elementary school teachers to experiment with to teach factoring.

Examples

			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).
EKG-3:  3, 6, 2, 4, 8, 10, 5, 15, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11...
EKG-6:  6, 2, 4, 8, 10, 5, 15, 3, 9, 12, 14, 7, 21, 18, 16, 20, 22, 11...
EKG-9:  9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11...
EKG-12: 12, 2, 4, 6, 3, 9, 15, 5, 10, 8, 14, 7, 21, 18, 16, 20, 22, 11...
EKG-5:  5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11...
Of these, the smallest EKG sequence is numbered 3 so a(5) = 3.

Links

Crossrefs

A255198 records the number of closest neighbors.
For examples of EKG-n, see A064413, A169841, A169837, A169843, A169855, A169849.
Cf. A255583.

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.

Original entry on oeis.org

1, 1, 1, 4, 1, 6, 2, 2, 5
Offset: 2

Views

Author

Gordon Hamilton, Feb 16 2015

Keywords

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.

Examples

			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).

Links

Crossrefs

Cf. A064413, A169837, A169841, A169843, A169849, A169857, A255583.
A255524 gives the smallest closest neighbor.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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