Does there exist an infinite sequence of primes $p_1, p_2, p_3, \dots $ for which, \[p_{n+1}=2p_n+1\]for each $n$?
Source: 2021 Israel National Olympiad P2
Tags: number theory, national olympiad
Does there exist an infinite sequence of primes $p_1, p_2, p_3, \dots $ for which, \[p_{n+1}=2p_n+1\]for each $n$?