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Erdős problem 145

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Let s1<s2<⋯s_1 < s_2 < \cdots be the sequence of squarefree numbers. Is it true that, for any α≥0\alpha\geq 0, lim⁡x→∞1x∑sn≤x(sn+1−sn)α \lim_{x\to\infty} \frac{1}{x}\sum_{s_n\leq x}(s_{n+1}-s_n)^\alpha exists?

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Problem row
sha256:56bff9331405e04c478420c2f60bd5aaecd09386f241f71d801bdbd224ffae05
Metadata
sha256:c2cd588bbe5ca59cb8ee646053f459b3443c9d19fc7c8a105a40be0ce6babc3d
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:65f25ba34f5aa4243d63364f0d44ddd15422665d8c6538e1c8c7af9ac41889ae
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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