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A330556
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a(n) = (number of primes p <= 2*n+1 with Delta(p) == 2 mod 4) - (number of primes p <= 2*n+1 with Delta(p) == 0 mod 4), where Delta(p) = nextprime(p) - p.
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10
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0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 4, 4, 4, 3, 3, 4, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 7, 6, 6, 7, 8, 8, 8, 7, 7, 8, 8, 8, 7, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 7, 8, 9, 9, 9, 9, 9, 10, 11, 11, 11, 12, 12, 12, 11, 11, 12, 12, 12, 13, 13, 13
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OFFSET
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0,3
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COMMENTS
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Since Delta(prime(n)) grows roughly like log n, this probably changes sign infinitely often. When is the next time a(n) is zero, or the first time a(n) < 0 (if these values exist)?
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LINKS
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EXAMPLE
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n=5, 2*n+1=11: there are three primes <= 11 with Delta(p) == 2 mod 4, namely 3,5,11; and one with Delta(p) == 0 mod 4, namely 7; so a(5) = 3-1 = 2.
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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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