Geodesic
On the subsequence of primes having prime subscripts
Journal of integer sequences, Tome 12 (2009) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We explore the subsequence of primes with prime subscripts, $(q_{n})$, and derive its density and estimates for its counting function. We obtain bounds for the weighted gaps between elements of the subsequence and show that for every positive integer $m$ there is an integer arithmetic progression $(an+b : n \in \Bbb N)$ with at least $m$ of the $(q_{n})$ satisfying $q_{n} = an+b$.
Classification : 11A41, 11B05, 11B25, 11B83
Keywords: prime-prime, prime-prime number theorem, prime-prime gaps, prime-primes in progressions 
@article{JIS_2009__12_2_a2,
     author = {Broughan, Kevin A. and Barnett, A.Ross},
     title = {On the subsequence of primes having prime subscripts},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
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     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_2_a2/}
}
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Broughan, Kevin A.; Barnett, A.Ross. On the subsequence of primes having prime subscripts. Journal of integer sequences, Tome 12 (2009) no. 2. http://geodesic.mathdoc.fr/item/JIS_2009__12_2_a2/