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 A365984 Starting with a(1) = 2, the lexicographically earliest infinite sequence of distinct positive integers such that |a(n) - a(n-1)| is a divisor of a(n), and where |a(n) - a(n-1)| > 1. 2
 2, 4, 6, 8, 10, 12, 9, 18, 15, 20, 16, 14, 21, 24, 22, 33, 30, 25, 50, 40, 32, 28, 26, 39, 36, 27, 54, 45, 42, 35, 70, 56, 48, 44, 46, 69, 66, 55, 60, 57, 38, 76, 72, 63, 84, 77, 88, 80, 64, 62, 93, 90, 75, 78, 52, 65, 130, 104, 91, 98, 96, 92, 94, 141, 138, 115, 110, 99, 102, 51, 34, 68, 85, 170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For the sequence to be infinite no term can be a prime except for a(1) = 2. One can easily show that if a(n) is a prime p, then the only possible value for a(n-1) or a(n+1) is 2p. If a(n) = p was a term then the difference between it and the previous term must also be p, implying the previous term is a multiple of p, so it must be 2p. As 2p has now already appeared the term after p would not exist, thus terminating the sequence. The first term that is not a prime power that cannot be used even though it satisfies being divisible by the difference between it and the previous term is 175, which appears to be a valid value for a(214) since a(213) = 350. However the next term after 175 would have to be one of 140, 150, 168, 170, 180, 182, 200, 210, 350, but all of those values have already appeared as previous terms, so 175 can never appear else it would terminate the sequence. LINKS Scott R. Shannon, Table of n, a(n) for n = 1..5000 a(4) = 8 as |8 - a(3)| = |8 - 6| = 2, and 2 is a divisor of 8. Note that 3 would also satisfy this requirement, but as shown above a prime will terminate the sequence so is not permitted. CROSSREFS Cf. A027750, A366111, A363576, A359799. Sequence in context: A055954 A366021 A365453 * A301454 A161602 A359496 Adjacent sequences: A365981 A365982 A365983 * A365985 A365986 A365987 KEYWORD nonn AUTHOR Scott R. Shannon, Sep 24 2023 STATUS approved

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Last modified August 11 07:51 EDT 2024. Contains 375059 sequences. (Running on oeis4.)