Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences

The Piatetski-Shapiro sequences are sequences of the form (⌊nc⌋)n=1∞{\left(\lfloor {n}^{c}\rfloor )}_{n=1}^{\infty } and the Beatty sequence is the sequence of integers (⌊αn+β⌋)n=1∞{(\lfloor \alpha n+\beta \rfloor )}_{n=1}^{\infty }. We prove that there are infinitely many Carmichael numbers composed of entirely the primes from the intersection of a Piatetski-Shapiro sequence and a Beatty sequence for c∈1,1913718746c\in \left(\phantom{\rule[-0.75em]{}{0ex}},1,\frac{19137}{18746}\right), α>1\alpha \gt 1 irrational and of finite type by investigating the Piatetski-Shapiro primes in arithmetic progressions in a Beatty sequence. Moreover, we also discuss the intersection of a Piatetski-Shapiro sequence and multiple Beatty sequences in arithmetic progressions.

Abstract licence: CC BY

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