A074819 Numbers k such that mu(k)+mu(k+1) = 0.

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

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

Cf. A008683, A092410.

Cf. A007674, A059956, A065474, A068781.

Sequence in context: A242731 A151976 A331199 * A330916 A113935 A279646

Adjacent sequences: A074816 A074817 A074818 * A074820 A074821 A074822

Keyword

nonn

Author

Benoit Cloitre, Sep 08 2002

Status

approved