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 A127567 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. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS http://h.xerol.org/f/1primecheck.txtShows applicable sequences of primes for n=2..9 EXAMPLE 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. MAPLE 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, Apr 13 2007 CROSSREFS Sequence in context: A084481 A006553 A054273 * A169643 A005993 A028247 Adjacent sequences:  A127564 A127565 A127566 * A127568 A127569 A127570 KEYWORD nonn AUTHOR Ellis M. Eisen (xerol(AT)xerol.org), Apr 02 2007 EXTENSIONS Corrected by Emeric Deutsch, Apr 13 2007 More terms from R. J. Mathar, Sep 23 2007 STATUS approved

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Last modified October 23 14:48 EDT 2018. Contains 316528 sequences. (Running on oeis4.)