Should that 1807 be 1806 ? There's a paper by Guy & Nowakowski, published long years ago in Delta (don't have the reference by me) Discovering Primes with Euclid, which discusses which primes arise in this kind of sequence. We had help from Lehmer & Selfridge, I remember. R. On Sat, 27 Jan 2007, Paul R. Pudaite wrote:
In the December 2006 issue of Am. Math. Monthly , Filip Saidak presents "A New Proof of Euclid's Theorem." Here's a concise rendition: Let f(x) = x^2 + x, let g[0] be a positive integer, and for n = 1, 2, 3, ..., let g[n] = f(g[n-1]). Then g[n] has at least n different prime factors. I omit the proof for those who might enjoy working it out for themselves.
The case of g[0] = 1 seems somewhat canonical. I'm curious about which primes appear as factors in the sequence of g[n] (2, 6, 42, 1807, ...). This sequence begins: 2, 3, 7, 13, 43, 73, 139, 181, 547, 607, 1033, 1171, ...
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