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A243937
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Even numbers n>=6 for which lpf(n-1) > lpf(n-3), where lpf = least prime factor.
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13
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6, 8, 12, 14, 18, 20, 24, 30, 32, 36, 38, 42, 44, 48, 54, 60, 62, 66, 68, 72, 74, 78, 80, 84, 90, 96, 98, 102, 104, 108, 110, 114, 120, 122, 126, 128, 132, 138, 140, 144, 150, 152, 156, 158, 162, 164, 168, 174, 180, 182, 186, 188, 192, 194, 198, 200, 204, 210
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OFFSET
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1,1
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COMMENTS
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Complement of A245024 over even n >= 6.
Conjecture: All differences are 2, 4 or 6 such that there are no two consecutive terms 2 (..., 2, 2, ...), no two consecutive terms 4, while consecutive terms 6 occur 1, 2, 3 or 4 times; also consecutive pairs of terms 2, 4 appear 1, 2, 3 or 4 times. The conjecture is verified up to n = 2.5*10^7. - Vladimir Shevelev and Peter J. C. Moses, Jul 11 2014
Divisibility by 3 means 6m is in the sequence for all m > 0, and 6m + 4 never is, while 6m + 2 is undetermined. Divisibility by 5 means 30m + 8 is always in the sequence, and 30m + 26 never is. This proves the above conjecture. - Jens Kruse Andersen, Aug 19 2014
Note that,
1) Since numbers of the form 6*k evidently are in the sequence, then the counting function of the terms not exceeding x is not less than x/6.
2) Sequence {a(n)-1} contains all primes greater than 3 in the natural order. The subsequence of other terms of {a(n)-1} is 35, 65, 77, 95, ... - Vladimir Shevelev, Jul 15 2014
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LINKS
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PROG
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(PARI) select(n->factor(n-1)[1, 1]>factor(n-3)[1, 1], vector(200, x, 2*x+4)) \\ Jens Kruse Andersen, Aug 19 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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