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Search: id:A141399
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| A141399 |
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A positive integer n is included if all the distinct primes that divide n and n+1 together are members of a set of consecutive primes. In other words, n is included if and only if n*(n+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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The smallest prime in the set of consecutive primes is always 2, since n*(n+1) is even.
No more terms less than 10^6. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 12 2008]
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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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); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 12 2008]
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CROSSREFS
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Cf. A073491.
Sequence in context: A058237 A009388 A125871 this_sequence A104737 A120057 A099422
Adjacent sequences: A141396 A141397 A141398 this_sequence A141400 A141401 A141402
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KEYWORD
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more,nonn
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AUTHOR
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Leroy Quet Aug 03 2008
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 12 2008
No further terms thru 5*10^8. [From Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2009]
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