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Infinitely many primes, and Mobius randomness in sparse sets
Problem 1: Find a (not extremely artificial) set A of integers so that for every $n$, $|A\cap [n]| \le n^{0.499}$, ($[n]=\{1,2,...,n\}$,) where you can prove that $A$ contains infinitely many...
View ArticleAnswer by Christian Elsholtz for Infinitely many primes, and Mobius...
Let me first comment on your examples:The record is acually $t=n^{0.525}$, due to Baker, Harman and Pintz.A slightly thinner sequence of this type is $n=a^3+2b^3$, investigated byHeath-Brown, and also...
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