### Abstract

Let {a_{i}} with a_{1} ≥ 2 be an infinite bounded sequence of positive integers, and d_{1} = 1, d_{i} = ±1 for i = 2, 3,.... Let {Q_{i}} be another sequence defined by the recursion Q_{1} = 1, Q_{i} = a_{i-1}Q_{i-1}^{k} for i = 2, 3,..., where k ≥ 2 an integer. Put C_{k}(a) = Σ_{i = 1}^{∞}d_{i}Q_{i}^{-1}. In this paper we shall determine the simple continued fraction expansion for the real numbers C_{k}(a).

Original language | English |
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Pages (from-to) | 232-236 |

Number of pages | 5 |

Journal | Journal of Number Theory |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1982 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Simple continued fractions for the Fredholm numbers.** / Pethő, A.

Research output: Contribution to journal › Article

*Journal of Number Theory*, vol. 14, no. 2, pp. 232-236. https://doi.org/10.1016/0022-314X(82)90048-8

}

TY - JOUR

T1 - Simple continued fractions for the Fredholm numbers

AU - Pethő, A.

PY - 1982

Y1 - 1982

N2 - Let {ai} with a1 ≥ 2 be an infinite bounded sequence of positive integers, and d1 = 1, di = ±1 for i = 2, 3,.... Let {Qi} be another sequence defined by the recursion Q1 = 1, Qi = ai-1Qi-1k for i = 2, 3,..., where k ≥ 2 an integer. Put Ck(a) = Σi = 1∞diQi-1. In this paper we shall determine the simple continued fraction expansion for the real numbers Ck(a).

AB - Let {ai} with a1 ≥ 2 be an infinite bounded sequence of positive integers, and d1 = 1, di = ±1 for i = 2, 3,.... Let {Qi} be another sequence defined by the recursion Q1 = 1, Qi = ai-1Qi-1k for i = 2, 3,..., where k ≥ 2 an integer. Put Ck(a) = Σi = 1∞diQi-1. In this paper we shall determine the simple continued fraction expansion for the real numbers Ck(a).

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U2 - 10.1016/0022-314X(82)90048-8

DO - 10.1016/0022-314X(82)90048-8

M3 - Article

VL - 14

SP - 232

EP - 236

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 2

ER -