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A089497
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mu(prime(n)+1) - mu(prime(n)-1), where mu is the Moebius function.
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3
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1, 1, -1, -1, 1, 0, 0, -1, -1, 1, 1, -1, 1, -1, 0, -1, 1, 1, 1, 1, 1, -1, 0, 0, -1, 1, -1, -1, -1, 0, 1, -1, 1, 0, 0, 1, 0, -1, -1, -1, -1, 1, 1, 0, 0, -1, 1, -1, -1, 0, 1, 0, 0, -1, -1, 0, 0, 1, -1, 1, 0, 0, 1, 1, -1, -1, 0, -1, 0, -1, -1, 1, -1, 0, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 0, 1, 1, -1, -1, -1, 0, 0, 1, -1, 1, 0, 0, 1, -1, 0, -1, 1, -1, 0, -1, 0
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OFFSET
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2,1
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COMMENTS
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This difference is always -1, 0 or 1 because for odd prime p, both p-1 and p+1 cannot be squarefree; one of them will be divisible by 4. This also implies that terms in this sequence are zero only for primes p such that mu(p-1) = mu(p+1) = 0, which is A075432.
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LINKS
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FORMULA
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Let p = prime(n), then a(n) = (-1/p) mu(p+(-1/p)), where (-1/p) is the Legendre symbol, A070750. (Pieter Moree)
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MATHEMATICA
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Table[MoebiusMu[Prime[n]+1] - MoebiusMu[Prime[n]-1], {n, 2, 150}]
MoebiusMu[#+1]-MoebiusMu[#-1]&/@Prime[Range[2, 110]] (* Harvey P. Dale, Sep 16 2018 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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