What about the sequence s_n = 12013n, n = 1,2,3,.... --Dan On 2013-06-26, at 5:23 PM, Keith F. Lynch wrote:
Last month, Zhang proved that there exists a number N such that there are infinitely many primes that differ from another prime by not more than N. (He showed that N is at most 70 million. That upper bound has since been reduced to 12,012. See http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_pri... )
I've wondered if the same is true for any monotonically increasing sequence of positive integers (i.e. no duplicate terms) for which the sum of the reciprocals diverges. Can anyone think of a counterexample?
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