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A372144
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Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(n+1), a(2*n+1) and a(2*n+2) have a common prime factor.
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3
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1, 2, 4, 6, 8, 10, 3, 9, 12, 14, 5, 15, 18, 21, 24, 27, 16, 20, 7, 28, 25, 30, 33, 36, 22, 26, 35, 42, 32, 34, 39, 45, 38, 40, 44, 46, 49, 56, 48, 50, 55, 60, 51, 54, 11, 66, 52, 58, 62, 64, 13, 65, 63, 70, 57, 69, 68, 72, 17, 85, 75, 78, 80, 90, 19, 76, 74
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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This sequence is a permutation of the positive integers with inverse A372185; the proof is similar to that for A370843.
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LINKS
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FORMULA
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GCD(a(n+1), a(2*n+1), a(2*n+2)) <> 1 for any n > 0.
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EXAMPLE
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The first terms, arranged alongside a binary tree where each parent node (except the root) and its children share some prime factor, are:
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1
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.-------2-------.
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.---4---. .---6---.
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.-8-. .10-. .-3-. .-9-.
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12 14 5 15 18 21 24 27
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PROG
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(PARI) \\ See Links section.
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CROSSREFS
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Cf. A372130 (analog without common prime factor), A372143 (analog based on binary 1's), A372185 (inverse).
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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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