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Bull. Austral. Math. Soc. 78 (2008), 431436 doi:10.1017/S0004972708000804ON THE DENSITY OF INTEGERS OF THE FORM ( p 1)2n IN ARITHMETIC PROGRESSIONS XUEGONG SUN and JINHUI FANG (Received 18 February 2008) Abstract Erdos and Odlyzko proved that odd integers k such that k2n + 1 is prime for some positive integer n have a positive lower density. In this paper, we characterize all arithmetic progressions in which natural numbers that can be expressed in the form ( p 1)2n (where
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