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Let us divide the prime numbers into bins. Prime p will go into bin
number floor(p/1000).
Let us pick a subset of the naturals by first selecting a set of bins, then taking all the naturals that have only primes inside the selected bins as their factors. (So, for example, to pick the number 3999991=1997*2003, we will need to first select at least both of bin number 1 [for 1997] and bin number 2 [for 2003]). The harmonic series is the sum of 1/n over n=1,2,... This series is known to diverge. By selecting a set of bins, we are effectively picking a subset of the naturals. Let us calculate the partial harmonic series that is calculated solely over this (infinite) subset. This month's question: what is the minimum number of bins that needs to be selected for the sub-series to diverge? Prove your answer. |
List of solvers:Hongcheng Zhu (1 April 13:11)Rani Hod (2 April 01:18) Omer Angel (2 April 02:03) Ross Millikan (3 April 06:23) Mark Tilford (5 April 02:48) Itsik Horovitz (15 April 17:15) Bojan Bašić (20 April 01:15) Albert Stadler (21 April 23:17) David Jager (29 April 00:11) |
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