Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.3

On the Subsequence of Primes Having Prime Subscripts

Kevin A. Broughan and A. Ross Barnett
University of Waikato
Hamilton, New Zealand


We explore the subsequence of primes with prime subscripts, (qn), 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 ∈ ℕ) with at least m of the (qn) satisfying qn = an+b.

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(Concerned with sequence A006450.)

Received December 5 2008; revised version received January 14 2009. Published in Journal of Integer Sequences, January 17 2009.

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