Geodesic
On Rowland's sequence
The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2
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E. S. Rowland proved that $a_k= a_{k-1}+ \gcd(k,a_{k-1})$, $a_1= 7$ implies that $a_{k}-a_{k-1}$ is always 1 or prime. Conjecturally this property also holds for any $a_1>3$ from a certain $k$ onwards. We state some properties of this sequence for arbitrary values of $a_1$. Namely, we prove that some specific sequences contain infinitely many primes and we characterize the possible finite subsequences of primes.
DOI : 10.37236/2006
Classification : 11A41, 11B37
Mots-clés : prime numbers, prime-generating sequence, Rowland's sequence 
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     author = {Fernando Chamizo and Dulcinea Raboso and Seraf{\'\i}n Ruiz-Cabello},
     title = {On {Rowland's} sequence},
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     year = {2011},
     volume = {18},
     number = {2},
     doi = {10.37236/2006},
     zbl = {1223.11008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2006/}
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Fernando Chamizo; Dulcinea Raboso; Serafín Ruiz-Cabello. On Rowland's sequence. The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2. doi: 10.37236/2006

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