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Nov 13, 2012 at 8:16 comment added joro Re: "tends to 1". I suppose in general it tends to 1. Repeatedly multiplying by 4 is exponential in 2. Unfortunately squaring $2n+1$ gives doubly exponential growth. Doubt the product of the smaller $n$ can compensate the doubly exponential growth. Well might be wrong.
Nov 13, 2012 at 6:16 comment added joro @Gerhard it is interesting how relatively big the 3-full part of n(n+1) can be. If it is sufficiently big it will disprove both this and the abc conjecture.
Nov 12, 2012 at 22:42 comment added Gerhard Paseman In fact this sequence deserves more attention. Can one prove that from the sequence (n,n+1) one has infinitely many prime members of (2n+1)? We may have the opportunity of putting two conjectures head-to-head. Gerhard "Ask Me About System Design" Paseman, 2012.11.12
Nov 12, 2012 at 22:21 comment added Gerhard Paseman The fact that you keep multiplying by 4 seems promising. Are you sure that sequence tends to 1? Gerhard "Ask Me About System Design" Paseman, 2012.11.12
Nov 12, 2012 at 15:13 history answered joro CC BY-SA 3.0