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A120627
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Least positive k such that both prime(n)+k and prime(n)+2k are prime, or 0 if no such k exists.
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6
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0, 2, 6, 6, 6, 24, 6, 12, 18, 12, 6, 30, 6, 18, 6, 18, 12, 6, 6, 18, 54, 24, 24, 12, 6, 6, 24, 30, 42, 18, 12, 18, 30, 12, 24, 6, 36, 18, 6, 54, 84, 30, 36, 18, 30, 12, 30, 54, 6, 42, 18, 12, 36, 6, 6, 48, 12, 6, 30, 36, 24, 54, 30, 36, 18, 36, 18, 30, 6, 24, 48, 30, 6, 24, 30, 18, 30
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OFFSET
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1,2
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COMMENTS
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Note that 6 divides a(n) for n>2. - T. D. Noe, Aug 29 2006
Van der Corput's theorem: There are infinitely many positive integers n, k such that n, n+nk, n+2nk are all prime. - Jonathan Vos Post, Apr 17 2007
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LINKS
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EXAMPLE
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a(3)=6 because prime(3)=5 and 5+6 and 5+12 are primes.
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MATHEMATICA
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f[n_] := Block[{p = Prime[n], k = 1}, If[n == 1, 0, While[ ! PrimeQ[p + 2k] || ! PrimeQ[p + 4k], k++ ]; 2k] ]; Table[f[n], {n, 80}] (* Ray Chandler, Aug 28 2006 *)
Join[{0}, Table[p=Prime[n]; k=2; While[ !PrimeQ[p+k] || !PrimeQ[p+2k], k=k+2]; k, {n, 2, 100}]] - T. D. Noe, Aug 29 2006
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PROG
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(PARI) a(n)=if(n<2, 0, my(p=prime(n), k); while(!isprime(p+k++)||!isprime(p+2*k), ); k) \\ Charles R Greathouse IV, Apr 24 2015
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CROSSREFS
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KEYWORD
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easy,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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