Continued fractions and irrationality exponents for modified engel and pierce series

An Engel series is a sum of reciprocals of a non-decreasing sequence (xn) of positive integers, which is such that each term is divisible by the previous one, and a Pierce series is an alternating sum of the reciprocals of a sequence with the same property. Given an arbitrary rational number, we show that there is a family of Engel series which when added to it produces a transcendental number ? whose continued fraction expansion is determined explicitly by the corresponding sequence (xn), where the latter is generated by a certain nonlinear recurrence of second order. We also present an analogous result for a rational number with a Pierce series added to or subtracted from it. In both situations (a rational number combined with either an Engel or a Pierce series), the irrationality exponent is bounded below by (3 + ?5)/2, and we further identify infinite families of transcendental numbers ? whose irrationality exponent can be computed precisely. In addition, we construct the continued fraction expansion for an arbitrary rational number added to an Engel series with the stronger property that x2j divides xj+1 for all j

Rhodnius barretti, a new species of Triatominae (Hemiptera: Reduviidae) from western Amazonia

Rhodnius barretti , a new triatomine species, is described based on adult specimens collected in rainforest environments within the Napo ecoregion of western Amazonia (Colombia and Ecuador). R. barretti resembles Rhodnius robustus s.l. , but mitochondrial cytochrome b gene sequences reveal that it is a strongly divergent member of the “robustus lineage”, i.e., basal to the clade encompassing Rhodnius nasutus , Rhodnius neglectus , Rhodnius prolixus and five members of the R. robustus species complex. Morphometric analyses also reveal consistent divergence from R. robustus s.l. , including head and, as previously shown, wing shape and the length ratios of some anatomical structures. R. barretti occurs, often at high densities, in Attalea butyracea and Oenocarpus bataua palms. It is strikingly aggressive and adults may invade houses flying from peridomestic palms. R. barretti must therefore be regarded as a potential Trypanosoma cruzi vector in the Napo ecoregion, where Chagas disease is endemic