### Abstract

For a set D of positive integers, a sequence {a_{1} < a _{2} < ⋯ a_{k}} is called an k-term D-diffsequence if a_{i} - a_{i-1} ∈ D for all i ∈ {2,..., k}. For a positive integer r, a set of positive integers D is r-accessible if every r-coloring of ℤ^{+} has arbitrarily long monochromatic D-diffsequences. The largest r such that D is r-accessible is called the degree of accessibility of D. It is already known that each odd translation of the set of primes, P + t, is 2-accessible. We offer new results on the accessibility of translations the primes. The main result is that for any c ≥ 2, the degree of accessibility of P + c does not exceed the smallest prime factor of c.

Original language | English (US) |
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Pages (from-to) | 207-214 |

Number of pages | 8 |

Journal | Utilitas Mathematica |

Volume | 82 |

State | Published - Jul 1 2010 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability

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## Cite this

*Utilitas Mathematica*,

*82*, 207-214.