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A074819
Numbers k such that mu(k)+mu(k+1) = 0.
2
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
OFFSET
1,2
COMMENTS
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
LINKS
Kaisa Matomäki, Maksym Radziwiłł and Terence Tao, Sign patterns of the Liouville and Möbius functions, Forum of Mathematics, Sigma, Vol. 4. (2016), e14.
FORMULA
a(n) seems to be asymptotic to c*n with c=3.7....
A092410(a(n)) = 0. - Reinhard Zumkeller, Sep 04 2015
MATHEMATICA
Select[Range[1, 300], MoebiusMu[#] + MoebiusMu[#+1] == 0&] (* Vaclav Kotesovec, Feb 16 2019 *)
PROG
(Haskell)
a074819 n = a074819_list !! (n-1)
a074819_list = filter ((== 0) . a092410) [1..]
-- Reinhard Zumkeller, Sep 04 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Sep 08 2002
STATUS
approved