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First differences of zero-sites (A028442) of Mertens's function A002321.
1

%I #12 Jun 09 2024 09:05:15

%S 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,

%T 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,

%U 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

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

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

%H Amiram Eldar, <a href="/A057639/b057639.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Differences[Position[Accumulate[Array[MoebiusMu,1500]],0]//Flatten] (* _Harvey P. Dale_, Nov 10 2016 *)

%o (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

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

%K nonn

%O 1,1

%A _Labos Elemer_, Oct 11 2000

%E Offset corrected by _Amiram Eldar_, Jun 09 2024