科研之友
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摘要
The Ulam sequence is defined as a(1) = 1, a(2) = 2, and a(n) being the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This givesUlam remarked that understanding the sequence, which has been described as quite erratic, seems difficult and indeed nothing is known. We report the empirical discovery of a surprising global rigidity phenomenon: there seems to exist a real approximate to 2.5714474995... such that . Indeed, for the first 10(7) elements of Ulam's sequence, The same phenomenon arises for some other initial conditions a(1), a(2): the distribution functions look very different from each other and have curious shapes. A similar but more subtle phenomenon seems to arise in Lagarias' variant of MacMahon's primes of measurement sequence.
- 出版日期2017
