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
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Plot of a(n)/n for n = 1..1300000.
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