mersenneforum.org Down to a perfect number
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 2014-12-23, 09:47 #1 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 7×911 Posts Down to a perfect number Among sequences containing only numbers less than 1.2e8, we have one of length 93 starting at 67825288 and ending in 6, and one of length 83 starting at 66499496 and ending in 8128. Ending in 496 seems harder (89416431, of length 10, is the longest under those conditions), because the only permissible remotely-long trail is via 607^2 608 652 492. Goldbach's Conjecture obviously lets you write arbitrarily long sequences if you're allowed arbitrarily large odd numbers (find p+q=N-1 with p,q prime; then the predecessor is pq) No aliquot sequence ends in 28. I can't find a predecessor for 33550336 other than 44655764, and I can't find a predecessor for 44655764. Last fiddled with by fivemack on 2014-12-23 at 09:48

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