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A141399
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A positive integer k is included if all the distinct primes that divide k and k+1 together are members of a set of consecutive primes. In other words, k is included if and only if k*(k+1) is contained in sequence A073491.
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1
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1, 2, 3, 5, 8, 9, 14, 15, 20, 24, 35, 80, 125, 224, 384, 440, 539, 714, 1715, 2079, 2400, 3024, 4374, 9800, 12375, 123200, 194480, 633555
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OFFSET
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1,2
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COMMENTS
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The smallest prime in the set of consecutive primes is always 2, since k*(k+1) is even.
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LINKS
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EXAMPLE
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20 is factored as 2^2 * 5^1. 21 is factored as 3^1 * 7^1. Since the distinct primes that divide 20 and 21 (which are 2,3,5,7) form a set of consecutive primes, then 20 is in the sequence.
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MAPLE
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with(numtheory): a:=proc(n) local F, m: F:=`union`(factorset(n), factorset(n+1)): m:=nops(F): if ithprime(m)=F[m] then n else end if end proc: seq(a(n), n=1..1000000); # Emeric Deutsch, Aug 12 2008
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CROSSREFS
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KEYWORD
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more,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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