OEIS A00057: Primes that divide all Fibonacci sequences

We explore OEIS sequence A00057, the primes p for which the first Fibonacci number divisible by p occurs at position p+1. Using 7 as a worked example, we illustrate the rule, then delve into its links with entry points (A000162), Pisano periods, and the question of infinitude (still open). We discuss observed congruence patterns (terms are 3 mod 4, and for n≥2 terms are 3 or 7 mod 20), and connections to Lucas and generalized Fibonacci sequences (A06414, A07936, A10635). The episode also surveys cross-references, the available 1,000-term table, and computational tools (Mathematica and PARI code) provided in the OEIS entry for further exploration.

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