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A282841
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Lexicographically earliest sequence of distinct terms such that a(n)=length of first run of multiples of prime(n) in this sequence.
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3
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1, 2, 3, 6, 4, 5, 10, 15, 7, 14, 21, 28, 35, 42, 8, 9, 11, 22, 33, 44, 12, 13, 26, 39, 52, 65, 16, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 18, 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 20, 23, 46, 69, 92, 115, 138, 161, 24, 25
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OFFSET
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1,2
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COMMENTS
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For any i>0, let R_i denote the first run of multiples of prime(i) in this sequence; several such runs can overlap.
The following table gives the index of the first term belonging to k runs, alongside the corresponding runs, for small values of k:
k n Runs
-- -------- ----
0 1 None
1 2 R_1
2 1533 R_37 and R_38
3 7693674 R_1534 to R_1536
4 7706584 R_1534 to R_1537
5 7738564 R_1535 to R_1539
6 7751486 R_1535 to R_1540
7 37170235 R_3302 to R_3308
8 43960552 R_3551 to R_3558
9 44051293 R_3552 to R_3560
10 44145862 R_3553 to R_3562
11 44236717 R_3554 to R_3564
If i<j, then R_i starts before R_j.
For any prime p, there is a multiple of p in this sequence (see A282842).
Conjectures:
- For any k, there is a term belonging to k runs.
- This sequence is a permutation of the natural numbers.
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LINKS
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EXAMPLE
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a(1)=1 fits the definition.
a(2)=2 fits the definition and introduces R_1; R_1 has length a(1)=1: a(3) must not be a multiple of 2.
a(3)=3 fits the definition and the constraint on R_1.
a(3) introduces R_2; R_2 has length a(2)=2: a(4) must be a multiple of 3, whereas a(5) must not be a multiple of 3.
a(3)=6 fits the definition and the constraint on R_2.
a(4)=4 fits the definition and the constraint on R_2.
a(5)=5 fits the definition and introduces R_3.
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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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