Template:Sequence of the Day for September 3

Intended for: September 3, 2011

Timetable

• First draft entered by Daniel Forgues on May 30, 2011 ✓
• Draft reviewed by Alonso del Arte on July 2, 2011 ✓
• Draft approved by Alonso del Arte on July 31, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

The following line marks the end of the <noinclude> ... </noinclude> section.

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A064413: EKG sequence or electrocardiogram sequence:

a (1) = 1, a (2) = 2

; for

n   ≥   3, a (n)

is the smallest positive integer not already used which shares a factor with

a (n  −  1)

.

{ 1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, 18, 14, 7, 21, 24, 16, 20, 22, 11, 33, ... }

When plotted as a connect-the-dots plot the sequence looks somewhat like an electrocardiogram (abbreviated “EKG” in medical circles), so this sequence became known as the EKG* sequence. Every positive integer appears exactly once: this is a permutation of the positive integers. At the same time, the primes appear in ascending order (and any odd prime

p

is preceded by

2 p

and followed by

3 p

). This sequence was discovered (or invented?) by Jonathan Ayres in 2001.

_______________
* Weisstein, Eric W., EKG Sequence, from MathWorld—A Wolfram Web Resource.