A319520 Starts of strictly increasing runs of 0's in Mertens's function A002321.

2, 39, 331, 422, 45371, 22898822, 871469945

Offset

1,1

Comments

a(n) is always squarefree.

It is not known whether this sequence is infinite. Sequence A045882 is infinite but it appears that increasing runs of consecutive nonsquarefree numbers thin out very quickly. The requirement that the runs consist of 0's is much stronger and makes it uncertain whether this sequence is also infinite.

Links

Table of n, a(n) for n=1..7.

Example

2 is a term because M(2) = 0.
39 is a term because M(39) = M(40) = 0.
331 is a term because M(331) = M(332) = M(333) = 0.
422 is a term because M(422) = ... = M(425) = 0.
45371 is a term because M(45371) = ... = M(45376) = 0.

Mathematica

With[{s = Map[Boole[# == 0] &, Accumulate@ Array[MoebiusMu, 10^5]]}, Union@ Array[SequencePosition[s, ConstantArray[1, #]][[1, 1]] &, 5]] (* Michael De Vlieger, Sep 26 2018 *)

Prog

(PARI) M=S=R=0; for(n=1, oo, if(!M+=moebius(n), S||S=n, S, n-S>R&&print1(S", ")+R=n-S; S=0)) \\ M. F. Hasler, Nov 23 2018

Crossrefs

Cf. A002321, A045882.

Sequence in context: A086338 A329552 A042683 * A209632 A266863 A245053

Adjacent sequences: A319517 A319518 A319519 * A319521 A319522 A319523

Keyword

nonn,more

Author

Torlach Rush, Sep 21 2018

Extensions

a(6)-a(7) from Amiram Eldar, Sep 26 2018

Status

approved