OFFSET
2,1
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.
LINKS
Eric Weisstein's World of Mathematics, Moebius Function
Eric Weisstein's World of Mathematics, Legendre Symbol
FORMULA
Let p = prime(n), then a(n) = (-1/p) mu(p+(-1/p)), where (-1/p) is the Legendre symbol, A070750. (Pieter Moree)
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
sign
AUTHOR
T. D. Noe, Nov 04 2003
STATUS
approved