## Abstract

Recently, there has been a sharp rise of interest in properties of digits primes. Here we study yet another question of this kind. Namely, we fix an integer base g ⩾ 2 and then for every infinite sequence

*D*={d_{i}}^{∞}_{i=0 }∈ {0,..., g - 1}^{∞}

of g-ary digits we consider the counting function ω_{D,g}(N) of integers n ⩽ N for which ∑^{n − 1} _{i = 0}d_{i}g^{i} is prime. We construct sequences *D *for which ω_{D,g}(N) grows fast enough, and show that for some constant ϑ_{g} < g there are at most O(ϑ^{N} _{g}) initial elements (d_{0}, …, d_{N − 1}) of *D* for which ω_{D,g}(N) = N + *O*(1). We also discuss joint arithmetic properties of integers and mirror reflections of their g-ary expansions.

Original language | English |
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Pages (from-to) | 184-192 |

Number of pages | 9 |

Journal | Experimental Mathematics |

Volume | 27 |

Issue number | 2 |

Early online date | 31 Oct 2016 |

DOIs | |

Publication status | Published - 2018 |

Externally published | Yes |

## Keywords

- digits
- primes
- SUM

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