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A281409
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Lexicographically first sequence of distinct terms, beginning with a(1)=5, with the property that each triple of consecutive terms contains a term that divides the sum of the other two terms.
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3
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5, 1, 2, 3, 4, 7, 9, 8, 10, 6, 14, 16, 12, 20, 28, 24, 13, 11, 15, 18, 21, 33, 27, 30, 19, 41, 22, 25, 47, 36, 58, 50, 42, 23, 61, 31, 32, 63, 65, 64, 43, 85, 44, 91, 45, 17, 40, 57, 74, 97, 51, 37, 60, 83, 106, 129, 152, 175, 109, 66, 35, 39, 82, 113, 133, 93
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OFFSET
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1,1
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COMMENTS
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The initial term a(1)=5 seems to be the least one that leads to a sequence that is not ultimately linear.
The variant with:
- a(1)=3 starts with 3, 1, 2, and then matches A000027,
- a(1)=4 starts with 4, 1, 2, and then matches A143097,
- a(1)=6 starts with 6, 1, 2, 3, 4, 5, and then matches A000027,
- a(1)=9 starts with 9, 1, 2, 3, 4, 5, 6, 7, 8, 13, 11, 12, 10, and then matches A143097.
Conjecturally, all other variants are not ultimately linear.
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LINKS
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EXAMPLE
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The first terms, alongside the indexes of the terms that divide the sum of the other two terms within the n-th triple of consecutive terms, are:
n a(n) Indexes
-- ---- -------
1 5 2, 3
2 1 1, 2, 3
3 2 2
4 3 3
5 4 1
6 7 3
7 9 1
8 8 1, 3
9 10 1, 2
10 6 1
11 14 1
12 16 1, 2
13 12 1, 2
14 20 3
15 28 3
16 24 1
17 13 1
18 11 1
19 15 2
20 18 1
21 21 3
22 33 3
23 27 3
24 30 1
25 19 2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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