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A317595
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a(n) is the number of primes between 2n and the largest prime p such that 2n-p is also a prime.
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1
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1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 3, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0
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OFFSET
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2,48
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COMMENTS
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If the Goldbach Conjecture is true, this sequence is defined for n >= 2.
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LINKS
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FORMULA
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EXAMPLE
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For n=2, 2n=4 = 2+2, there is one prime, which is 3, between 2 and 4. So a(2)=1;
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For n=8, 2n=16 = 13+3, there is no prime between 13 and 16. So a(8)=0;
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For n=49, 2n=98 = 79+19, there are three primes, 83, 89, and 97 between 79 and 98 such that the difference of 98 and these primes, 15, 9, and 1 respectively, are not prime. So a(49)=3.
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MATHEMATICA
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Table[n2 = n*2; p = NextPrime[n2]; ct = 0; While[p = NextPrime[p, -1]; ! PrimeQ[n2 - p], ct++]; ct, {n, 2, 88}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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