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Search: id:A127567
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| A127567 |
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Given k, the product of the first n primes and starting with the first prime at least 3 greater than k, a(n) is the number of consecutive primes where p-k is also prime. |
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2
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| 2, 6, 10, 19, 25, 29, 36, 42, 43, 41, 63, 65, 45, 69, 86, 98, 90, 77, 94, 132, 118, 112, 132, 120, 131, 133, 150, 128, 203, 220, 163, 175, 161, 176, 168, 171, 206, 233, 236, 250, 201, 230, 293, 270, 297, 283, 256, 253, 272, 318, 266, 277, 296, 308, 349, 353, 312
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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http://h.xerol.org/f/1primecheck.txtShows applicable sequences of primes for n=2..9
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EXAMPLE
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For n = 2, k = 2*3 = 6. The first prime at least 3 greater than 6 is 11.
11-6 = 5, 13-6 = 7, 17-6 = 11, 19-6 = 13, 23-6 = 17, 29-6 = 23, all of which are primes. 31-6 = 25 is not prime, so a(2) = 6 because there are 6 prime terms.
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MAPLE
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with(numtheory): a:=proc(n) local k, p, c, ct, j: k:=product(ithprime(i), i=1..n); p:=nextprime(k+2); c:=pi(p): ct:=0: for j from c while isprime(ithprime(j)-k)=true do ct:=ct+1: od: ct; end: seq(a(n), n=1..9); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 13 2007
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CROSSREFS
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Sequence in context: A084481 A006553 A054273 this_sequence A005993 A028247 A065054
Adjacent sequences: A127564 A127565 A127566 this_sequence A127568 A127569 A127570
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KEYWORD
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nonn
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AUTHOR
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Ellis M. Eisen (xerol(AT)xerol.org), Apr 02 2007
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EXTENSIONS
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Corrected by Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 13 2007
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 23 2007
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