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- W2890748511 abstract "The results for the fractional sequence $left {[x/n]+1:n leq xright }$, and the fractional sequence in arithmetic progression $left {q[x/n]+a:n leq xright }$, where $a<q$ are integers such that $gcd(a,q)=1$, prove that these sequences of fractional numbers contain the set of primes, and the set primes in arithmetic progressions as $x to infty$ respectively. Furthermore, the corresponding error terms for these sequences are improved. Other results considered are the fractional sequences of integers such as the sequence $left {[x/n]^2+1:n leq xright }$ generated by the quadratic polynomial $n^2+1$, and the sequence $left {[x/n]^3+2:n leq xright }$ generated by the cubic polynomial $n^3+2$. It is shown that each of these sequences of fractional numbers contains infinitely many primes as $x to infty$." @default.
- W2890748511 created "2018-09-27" @default.
- W2890748511 creator A5040810155 @default.
- W2890748511 date "2018-09-08" @default.
- W2890748511 modified "2023-10-18" @default.
- W2890748511 title "Primes In Fractional Sequences" @default.
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- W2890748511 doi "https://doi.org/10.48550/arxiv.1809.02821" @default.
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