A057639 First differences of zero-sites (A028442) of Mertens's function A002321.

37, 1, 18, 7, 28, 8, 44, 4, 1, 9, 1, 3, 1, 2, 48, 17, 1, 3, 1, 2, 16, 75, 2, 1, 1, 20, 2, 1, 2, 4, 1, 1, 2, 27, 8, 2, 1, 1, 2, 1, 5, 1, 5, 1, 2, 1, 1, 1, 2, 1, 109, 4, 66, 1, 27, 1, 1, 144, 4, 8, 2, 1, 2, 13, 1, 2, 9, 1, 1, 24, 1, 3, 16, 8, 6, 1, 2, 3, 4, 2, 1, 2, 5, 1, 2, 4, 3, 2, 1, 3, 1, 82, 3, 5

Offset: 1

Author

Labos Elemer, Oct 11 2000

Keywords

• nonn

Comments

Mertens's function (A002321) is oscillating. The width of its waves is given here.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002321, A013928, A028442, A013940, A051400, A051401, A051402.

Programs

Mathematica

Differences[Position[Accumulate[Array[MoebiusMu,1500]],0]//Flatten] (* Harvey P. Dale, Nov 10 2016 *)

PARI

lista(kmax) = {my(s = 0, k1 = 2); for(k2 = 3, kmax, s += moebius(k2); if(s == 0, print1(k2 - k1, ", "); k1 = k2));} \\ Amiram Eldar, Jun 09 2024

Formula

a(n) = A028442(n+1) - A028442(n).

Extensions

Offset corrected by Amiram Eldar, Jun 09 2024