Wilf's Sequence
Perhaps the best known primefree sequence is the one found by Herbert Wilf, with initial terms
- a1 = 20615674205555510, a2 = 3794765361567513 (sequence A083216 in OEIS).
The proof that every term of this sequence is composite relies on the periodicity of Fibonacci-like number sequences modulo the members of a finite set of primes. For each prime p, the positions in the sequence where the numbers are divisible by p repeat in a periodic pattern, and different primes in the set have overlapping patterns that result in a covering set for the whole sequence.
Read more about this topic: Primefree Sequence
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