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%I #21 Sep 09 2022 04:19:50
%S 1,5,6,8,10,13,22,24,27,37,44,46,48,49,58,61,63,65,69,73,75,77,80,82,
%T 98,99,105,106,110,114,116,120,124,125,129,135,147,152,154,157,165,
%U 166,168,171,175,178,182,185,186,188,193,194,207,210,221,224,226,237,242
%N Numbers k such that mu(k)+mu(k+1) = 0.
%C 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
%H Reinhard Zumkeller, <a href="/A074819/b074819.txt">Table of n, a(n) for n = 1..10000</a>
%H Vaclav Kotesovec, <a href="/A074819/a074819.jpg">Plot of a(n)/n for n = 1..1300000</a>.
%H Kaisa Matomäki, Maksym Radziwiłł and Terence Tao, <a href="https://doi.org/10.1017/fms.2016.6">Sign patterns of the Liouville and Möbius functions</a>, Forum of Mathematics, Sigma, Vol. 4. (2016), e14.
%F a(n) seems to be asymptotic to c*n with c=3.7....
%F A092410(a(n)) = 0. - _Reinhard Zumkeller_, Sep 04 2015
%t Select[Range[1, 300], MoebiusMu[#] + MoebiusMu[#+1] == 0&] (* _Vaclav Kotesovec_, Feb 16 2019 *)
%o (Haskell)
%o a074819 n = a074819_list !! (n-1)
%o a074819_list = filter ((== 0) . a092410) [1..]
%o -- _Reinhard Zumkeller_, Sep 04 2015
%Y Cf. A008683, A092410.
%Y Cf. A007674, A059956, A065474, A068781.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Sep 08 2002
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