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A218769
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Let (p,p+2) be the n-th twin prime pair. a(n) is the least integer r > 1 for which the interval (r*p, r*(p+2)) contains no primes, or a(n)=0, if no such r exists.
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3
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0, 0, 0, 0, 4, 0, 2, 2, 2, 2, 3, 2, 5, 5, 4, 5, 4, 4, 3, 2, 2, 4, 4, 2, 2, 2, 6, 3, 3, 4, 3, 2, 3, 2, 2, 7, 3, 3, 2, 2, 2, 6, 0, 3, 2, 2, 5, 5, 23, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 5, 2
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OFFSET
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1,5
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COMMENTS
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For n<=20000, the largest a(n) is a(49)=23. a(n)=0 for n = 1, 2, 3, 4, 6, 43, 37890, 606457, ... corresponding to the twin primes (p, p+2) with p=3, 5, 11, 17, 41, 1277, 5995727, 143556431, ....
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LINKS
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EXAMPLE
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The 13th twin prime pair is {179, 181}. For r = 2 the range {358, ..., 362} contains prime 359; for r = 3, the range {537, ..., 543} contains prime 541; for r = 4, the range {716, ..., 724} contains prime 719. But for r = 5, the range {895, ..., 905} does not contain any prime. Thus a(13) = 5.
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MATHEMATICA
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rmax = 100; p1[1] = 3; p1[n_] := p1[n] = (p = NextPrime[p1[n-1]]; While[ !PrimeQ[p+2], p = NextPrime[p]]; p); a[n_] := Catch[ For[r = 2, r <= rmax, r++, If[ PrimePi[r*p1[n]] == PrimePi[r*(p1[n] + 2)], Throw[r], If[r == rmax, Throw[0]]]]]; Table[ a[n] , {n, 1, 65}] (* Jean-François Alcover, Dec 13 2012 *)
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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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