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A330647
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Lexicographically earliest sequence of distinct positive terms with an associate sequence t such that a(1) = t(1) = 1 and for n > 1, either a(n) divides t(n-1) (and in that case set t(n) = t(n-1)/a(n)) or a(n) is coprime to t(n-1) (and in that case set t(n) = t(n-1)*a(n)).
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2
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1, 2, 3, 5, 6, 4, 7, 9, 10, 11, 13, 14, 8, 12, 17, 19, 22, 16, 23, 24, 15, 26, 28, 20, 21, 18, 25, 29, 30, 31, 32, 34, 37, 38, 40, 35, 41, 43, 44, 33, 27, 36, 47, 52, 39, 46, 51, 42, 48, 49, 53, 56, 58, 59, 61, 64, 60, 45, 62, 63, 57, 67, 68, 71, 73, 74, 77
(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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All prime numbers appear in the sequence, in ascending order.
This sequence is likely a permutation of the natural numbers.
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LINKS
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EXAMPLE
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The first terms, alongside the corresponding t(n), are:
n a(n) t(n)
-- ---- ----
1 1 1
2 2 2
3 3 6
4 5 30
5 6 5
6 4 20
7 7 140
8 9 1260
9 10 126
10 11 1386
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MATHEMATICA
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Nest[Append[#1, Block[{k = 2, s}, While[Nand[FreeQ[#1[[All, 1]], k], MemberQ[{1, k}, Set[s, GCD[#3, k]]]], k++]; {k, If[s == 1, #3 k, #3/k]}]] & @@ {#, #[[-1, 1]], #[[-1, -1]]} &, {{1, 1}}, 66][[All, 1]] (* Michael De Vlieger, Dec 23 2019 *)
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A330648 for the corresponding sequence t.
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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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