Geodesic
A few new facts about the EKG sequence
Journal of integer sequences, Tome 11 (2008) no. 4
The EKG sequence is defined as follows: $a_1=1, a_2=2$ and $a_n$ is the smallest natural number satisfying $\gcd (a_{n-1}, a_n) > 1$ not already in the sequence. The sequence was previously investigated by Lagarias, Rains and Sloane. In particular, we know that $(a_n)$ is a permutation of the natural numbers and that the prime numbers appear in this sequence in an increasing order.
Classification : 11B83
Keywords: EKG sequence, integer sequence, prime numbers 
@article{JIS_2008__11_4_a2,
     author = {Hofman,  Piotr and Pilipczuk,  Marcin},
     title = {A few new facts about the {EKG} sequence},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {4},
     zbl = {1204.11057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_4_a2/}
}
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Hofman,  Piotr; Pilipczuk,  Marcin. A few new facts about the EKG sequence. Journal of integer sequences, Tome 11 (2008) no. 4. http://geodesic.mathdoc.fr/item/JIS_2008__11_4_a2/