# Odd prime values of the Ramanujan tau function

@article{Lygeros2013OddPV,
title={Odd prime values of the Ramanujan tau function},
author={Nik Lygeros and Olivier Rozier},
journal={The Ramanujan Journal},
year={2013},
volume={32},
pages={269-280}
}
• Published 15 March 2013
• Mathematics, Computer Science
• The Ramanujan Journal
We study the odd prime values of the Ramanujan tau function, which form a thin set of large primes. To this end, we define LR(p,n):=τ(pn−1) and we show that the odd prime values are of the form LR(p,q) where p,q are odd primes. Then we exhibit arithmetical properties and congruences of the LR numbers using more general results on Lucas sequences. Finally, we propose estimations and discuss numerical results on pairs (p,q) for which LR(p,q) is prime.
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