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Erdős problem 287

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Let k≥2k\geq2. Is it true that, for any distinct integers 1<n1<⋯<nk1 < n_1 < \cdots < n_k such that ∑i=1k1ni=1\sum_{i=1}^k \frac{1}{n_i} = 1, we must have max⁡(ni+1−ni)≥3\max(n_{i+1} - n_i) \geq 3?

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Problem row
sha256:479e6e8d96083fc6840117b53c0156abdad4b096efb3c7dbbcb7c51cf2808e67
Metadata
sha256:6f2d53b73d22aa74b77a6ac52164277c2a3fad8b1c0a51753ee58d95f48902db
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:b9b8b0f9b4521b3bf7675b0dd0a93473ce7e9f34bb2ae5499aecb740a80887ef
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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