| 10 | Sums of Primes and Quadratic Linear Recurrence Sequences显示文摘Let U be a sequence of positive integers which grows essentially as a geometric progression. We give a criterion on U in terms of its distribution modulo d, d = 1, 2,..., under which the set of positive integers expressible by the sum of a prime number and an element of U has a positive lower density. This criterion is then checked for some second order linear recurrence sequences. It follows, for instance, that the set of positive integers of the formp+(2 + √ 3)n, wherepis a prime number andnis a positive integer, has a positive lower density. This generalizes a recent result of Enoch Lee. In passing, we show that the periods of linear recurrence sequences of ordermmodulo a prime number pcannot be 'too small' for most prime numbersp. | Artūras DUBICKAS | 2013 | Acta Mathematica Sinica,English Series2013，29，12： | 0 |
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