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A285487
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Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 5 distinct prime factors.
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9
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1, 2310, 2, 1155, 4, 1365, 6, 385, 12, 455, 18, 595, 22, 105, 26, 165, 14, 195, 28, 255, 38, 210, 11, 390, 7, 330, 13, 420, 17, 462, 5, 546, 10, 231, 20, 273, 30, 77, 60, 91, 66, 35, 78, 55, 42, 65, 84, 85, 114, 70, 33, 130, 21, 110, 39, 140, 51, 154, 15, 182
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OFFSET
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1,2
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COMMENTS
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This sequence can always be extended with a multiple of 2310 = 2*3*5*7*11; after a term that has at least 5 distinct prime factors, we can extend the sequence with the least unused number; as there are infinitely many numbers with at least 5 distinct prime factors, this sequence is a permutation of the natural numbers (with inverse A285488).
Conjecturally, a(n) ~ n.
The first fixed points are: 1, 75, 295, 375, 1205, 1207, 1211, 6017, 19870, 19872, 19874, 19878, 19907, 19909.
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LINKS
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EXAMPLE
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The first terms, alongside the primes p dividing a(n)*a(n+1), are:
n a(n) p
-- ---- --------------
1 1 2, 3, 5, 7, 11
2 2310 2, 3, 5, 7, 11
3 2 2, 3, 5, 7, 11
4 1155 2, 3, 5, 7, 11
5 4 2, 3, 5, 7, 13
6 1365 2, 3, 5, 7, 13
7 6 2, 3, 5, 7, 11
8 385 2, 3, 5, 7, 11
9 12 2, 3, 5, 7, 13
10 455 2, 3, 5, 7, 13
11 18 2, 3, 5, 7, 17
12 595 2, 5, 7, 11, 17
13 22 2, 3, 5, 7, 11
14 105 2, 3, 5, 7, 13
15 26 2, 3, 5, 11, 13
16 165 2, 3, 5, 7, 11
17 14 2, 3, 5, 7, 13
18 195 2, 3, 5, 7, 13
19 28 2, 3, 5, 7, 17
20 255 2, 3, 5, 17, 19
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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