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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| 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
| Eric Weisstein's World of Mathematics, Moebius Function
Eric Weisstein's World of Mathematics, Legendre Symbol
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FORMULA
| 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
| Table[MoebiusMu[Prime[n]+1] - MoebiusMu[Prime[n]-1], {n, 2, 150}]
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CROSSREFS
| Cf. A089451 (mu(p-1) for prime p), A089495 (mu(p+1) for prime p), A089496 (mu(p+1)+mu(p-1) for prime p).
Sequence in context: A014079 A071032 A071034 * A089496 A114592 A140653
Adjacent sequences: A089494 A089495 A089496 * A089498 A089499 A089500
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KEYWORD
| sign
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Nov 04 2003
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