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A288164
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Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n)*a(n+2) has at least 5 distinct prime factors.
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3
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1, 2, 2310, 1155, 3, 4, 770, 1365, 6, 8, 385, 1785, 12, 10, 455, 231, 18, 20, 595, 273, 22, 30, 105, 77, 26, 60, 165, 91, 14, 66, 195, 35, 28, 78, 255, 55, 38, 42, 210, 65, 11, 84, 390, 85, 7, 114, 330, 70, 13, 33, 420, 130, 17, 21, 462, 110, 5, 39, 546, 140
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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 natural numbers, with inverse A288799.
Conjecturally, a(n) ~ n.
For k >= 0, let f_k be the lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n)*a(n+k) has at least 5 distinct prime factors.
In particular, we have:
- f_0 = the numbers with at least 5 distinct prime factors,
- f_2 = a (this sequence),
If k > 0, then:
- f_k is a permutation of the natural numbers,
- f_k(i) = i for any i <= k,
- conjecturally, f_k(n) ~ n.
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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+2), are:
n a(n) p
-- ---- --------------
1 1 2, 3, 5, 7, 11
2 2 2, 3, 5, 7, 11
3 2310 2, 3, 5, 7, 11
4 1155 2, 3, 5, 7, 11
5 3 2, 3, 5, 7, 11
6 4 2, 3, 5, 7, 13
7 770 2, 3, 5, 7, 11
8 1365 2, 3, 5, 7, 13
9 6 2, 3, 5, 7, 11
10 8 2, 3, 5, 7, 17
11 385 2, 3, 5, 7, 11
12 1785 2, 3, 5, 7, 17
13 12 2, 3, 5, 7, 13
14 10 2, 3, 5, 7, 11
15 455 2, 3, 5, 7, 13
16 231 2, 3, 5, 7, 11
17 18 2, 3, 5, 7, 17
18 20 2, 3, 5, 7, 13
19 595 2, 5, 7, 11, 17
20 273 2, 3, 5, 7, 13
21 22 2, 3, 5, 7, 11
22 30 2, 3, 5, 7, 11
23 105 2, 3, 5, 7, 13
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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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