Geodesic
The Yellowstone permutation
Journal of integer sequences, Tome 18 (2015) no. 6
Define a sequence of positive integers by the rule that $a(n) = n$ for $1 \le n \le 3$, and for $n \ge 4, a(n)$ is the smallest number not already in the sequence which has a common factor with $a(n - 2)$ but is relatively prime to $a(n - 1)$. We show that this is a permutation of the positive integers. The remarkable graph of this sequence consists of runs of alternating even and odd numbers, interrupted by small downward spikes followed by large upward spikes, suggesting the eruption of geysers in Yellowstone National Park. On a larger scale the points appear to lie on infinitely many distinct curves. There are several unanswered questions concerning the locations of these spikes and the equations for these curves.
Classification : 11B83, 11Bxx, 11B75
Keywords: number sequence, EKG sequence, permutation of natural numbers 
@article{JIS_2015__18_6_a4,
     author = {Applegate,  David L. and Havermann,  Hans and Selcoe,  Robert G. and Shevelev,  Vladimir and Sloane,  N.J.A. and Zumkeller,  Reinhard},
     title = {The {Yellowstone} permutation},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {6},
     zbl = {1332.11031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a4/}
}
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AU  - Applegate,  David L.
AU  - Havermann,  Hans
AU  - Selcoe,  Robert G.
AU  - Shevelev,  Vladimir
AU  - Sloane,  N.J.A.
AU  - Zumkeller,  Reinhard
TI  - The Yellowstone permutation
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IS  - 6
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a4/
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%A Havermann,  Hans
%A Selcoe,  Robert G.
%A Shevelev,  Vladimir
%A Sloane,  N.J.A.
%A Zumkeller,  Reinhard
%T The Yellowstone permutation
%J Journal of integer sequences
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%N 6
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a4/
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%F JIS_2015__18_6_a4
Applegate,  David L.; Havermann,  Hans; Selcoe,  Robert G.; Shevelev,  Vladimir; Sloane,  N.J.A.; Zumkeller,  Reinhard. The Yellowstone permutation. Journal of integer sequences, Tome 18 (2015) no. 6. http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a4/