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A074819
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Numbers k such that mu(k)+mu(k+1) = 0.
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2
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1, 5, 6, 8, 10, 13, 22, 24, 27, 37, 44, 46, 48, 49, 58, 61, 63, 65, 69, 73, 75, 77, 80, 82, 98, 99, 105, 106, 110, 114, 116, 120, 124, 125, 129, 135, 147, 152, 154, 157, 165, 166, 168, 171, 175, 178, 182, 185, 186, 188, 193, 194, 207, 210, 221, 224, 226, 237, 242
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OFFSET
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1,2
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COMMENTS
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This sequence has a an asymptotic density (Matomäki et al., 2016). The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 5, 26, 274, 2673, 26909, 267872, 2680091, 26810993, 268098678, 2680989431, 26809725312, ... . This empirically indicates that the density is 0.26809... . This sequence is a disjoint union of A068781 whose density is 1 - 2 * A059956 + A065474, and the subsequence of A007674 of terms k with mu(k) and mu(k+1) having opposite signs. Assuming that this subsequence has a density which is exactly half the density of A007674, we get that this sequence has the density 1 - 12/Pi^2 + (3/2)*A065474 = 0.2680969447... . - Amiram Eldar, Sep 09 2022
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LINKS
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FORMULA
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a(n) seems to be asymptotic to c*n with c=3.7....
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MATHEMATICA
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Select[Range[1, 300], MoebiusMu[#] + MoebiusMu[#+1] == 0&] (* Vaclav Kotesovec, Feb 16 2019 *)
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PROG
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(Haskell)
a074819 n = a074819_list !! (n-1)
a074819_list = filter ((== 0) . a092410) [1..]
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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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