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A340779
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a(1)=1, a(2)=2; for n>=3, a(n) = the closest number to a(n-1) that has not occurred earlier and has at least one common factor with a(n-1), but none with a(n-2). In case of a tie, choose the smaller.
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0
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1, 2, 6, 15, 35, 28, 26, 39, 33, 22, 20, 45, 51, 34, 38, 57, 63, 56, 58, 87, 93, 62, 68, 85, 75, 72, 74, 185, 175, 168, 166, 415, 405, 402, 404, 505, 495, 492, 494, 481, 407, 396, 394, 985, 975, 972, 974, 2435, 2425, 2328, 2326, 5815, 5805, 5802, 5804, 7255, 7245, 7242, 7244, 9055
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OFFSET
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1,2
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COMMENTS
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The sequence uses a similar selection rule to the Enots Wolley sequence A336957 but instead of choosing the smallest number that has not occurred earlier that has a common factor with a(n-1) and no common factor with a(n-2), the number closest to a(n-1) that satisfies these rules is selected for a(n). If two such numbers are the same distance from a(n-1) then the smaller is chosen. Like A336957 for the sequence to continue a(n) must always have a prime factor not in a(n-1), thus a(n) cannot be a prime or a prime power.
The sequence grows sporadically with n, showing regions of little growth followed by a large jump due to the next term being the multiple of a large prime of the previous term. However due to the overall rapid increase in the terms it is very unlikely any fixed points exist.
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LINKS
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EXAMPLE
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a(5) = 35 as a(4) = 15 = 3*5 and a(3) = 6 = 2*3, thus a(5) must be a multiple of 5 while not being a multiple of 3, and must have a prime factor other than 5. The smallest unused number closest to 15 satisfying these criteria is 35.
a(6) = 28 as a(5) = 35 = 5*7 and a(4) = 15 = 3*5, this a(6) must be a multiple of 7 while not being a multiple of 5, and must have a prime factor other than 7. The smallest number satisfying these criteria is 14. However 28 also does and is only 7 away from a(5), while 14 is 21 away, thus 28 is chosen. This is the first term that differs from A336957.
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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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