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arXiv · 2604.20014

Explicit Prime Densities for Lucas Sequence Rank Divisibility

Joaquim Cera Da Conceição
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Abstract

Let $U$ be a Lucas sequence, $p$ be a prime, and $\rho_U(p)$ be the rank of appearance of $p$ in $U$, that is, the least positive integer $n$ such that $p\mid U_n$, if it exists. We derive closed-form formulas for the Dirichlet density of primes $p$ for which $d\mid \rho_U(p)$, where $d\geq 1$ is a fixed integer. Our results complete the work of Sanna ($2022$) by covering all $U$ and all $d\geq 1$.

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Joaquim Cera Da Conceição. 2026-04-21. Explicit Prime Densities for Lucas Sequence Rank Divisibility. https://arxiv.org/abs/2604.20014

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