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

1,1

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A215258 A176795 A272725 * A190356 A051316 A278067

Adjacent sequences: A057636 A057637 A057638 * A057640 A057641 A057642

Keyword

nonn

Author

Labos Elemer, Oct 11 2000

Extensions

Offset corrected by Amiram Eldar, Jun 09 2024

Status

approved