On digital distribution in some integer sequences
- 1 August 1965
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 5 (3) , 325-330
- https://doi.org/10.1017/s1446788700027750
Abstract
Although the harmonic series diverges, there is a sense in which it “nearly converges”. Let N denote the set of all positive integers, and S a subset of N. Then there are various sequences S for which converges, but for which the “omitted sequence” N–S is, in intuitive sense, sparse, compared with N. For example, Apostol [1] (page 384) quotes, without proof the case where S is the set of all Positive integers whose decimal representation does not invlove the digit zero (e.g. 7∈S but 101 ∉ S); then (1) converges, with T < 90.Keywords
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