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A137876
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a(n) = (nextprime(18n)-previousprime(18n))/2.
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4
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1, 3, 3, 1, 4, 1, 7, 5, 3, 1, 1, 6, 3, 3, 1, 5, 7, 7, 5, 4, 3, 4, 5, 1, 4, 6, 4, 3, 1, 9, 3, 3, 3, 3, 6, 3, 6, 4, 4, 4, 3, 3, 7, 5, 1, 1, 7, 7, 1, 10, 4, 4, 7, 3, 4, 6, 5, 5, 1, 9, 3, 4, 11, 1, 4, 3, 6, 3, 6, 9, 1, 3, 6, 17, 17, 3, 9, 5, 7, 4, 3, 5, 3, 6, 4, 3, 4, 7, 3, 1, 10, 10, 12, 12, 6, 5, 3, 9, 3, 6, 6
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OFFSET
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1,2
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COMMENTS
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a(n)=1 if 18n -/+ 1 are twin primes. Corresponding n's are in A137877.
Note that a(n) cannot be 2 (because, for arbitrary number m, if (6*m-1) is prime then (6*m+3) is not, and similarly, if (6*m+1) is prime then (6*m-3) is not). I conjecture that all other values are possible and a(n) == 0 (mod 3) are (much) more abundant.
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LINKS
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MAPLE
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seq((nextprime(18*n)-prevprime(18*n))/2, n=1..100); # Robert Israel, Apr 19 2015
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MATHEMATICA
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Table[(NextPrime[18 n] - NextPrime[18 n, -1]) / 2, {n, 100}] (* Vincenzo Librandi, Apr 19 2015 *)
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PROG
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(PARI) a(n) = (nextprime(18*n) - precprime(18*n))/2; \\ Michel Marcus, Oct 13 2013
(Magma) [(NextPrime(18*n)-PreviousPrime(18*n))/2: n in [1..100]]; // Vincenzo Librandi, Apr 19 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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