This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319520 #40 Mar 09 2025 12:28:53
%S A319520 2,39,331,422,45371,22898822,871469945,1319506393071,26296710367071
%N A319520 Starts of strictly increasing runs of 0's in Mertens's function A002321.
%C A319520 a(n) is always squarefree.
%C A319520 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.
%e A319520 2 is a term because M(2) = 0.
%e A319520 39 is a term because M(39) = M(40) = 0.
%e A319520 331 is a term because M(331) = M(332) = M(333) = 0.
%e A319520 422 is a term because M(422) = ... = M(425) = 0.
%e A319520 45371 is a term because M(45371) = ... = M(45376) = 0.
%t A319520 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 *)
%o A319520 (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
%Y A319520 Cf. A002321, A045882.
%K A319520 nonn,more
%O A319520 1,1
%A A319520 _Torlach Rush_, Sep 21 2018
%E A319520 a(6)-a(7) from _Amiram Eldar_, Sep 26 2018
%E A319520 a(8)-a(9) from _Henri Lifchitz_, Mar 09 2025