Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #38 Oct 01 2018 08:23:10
%S 165,237,330,354,357,365,402,406,421,426,794,797,813,885,894,897,905,
%T 914,1257,1281,1290,1298,1301,1337,1522,1526,1545,1842,1865,2094,2098,
%U 2118,2121,2137,4602,4609,4621,4629,4726,4729,4738,5106,5109,5198,5206,5221
%N Indices of Mertens's function M(n) (A002321) whose nearest neighbors have value 0.
%C This sequence records the shortest intervals where M(n) leaves 0 before returning to 0.
%C a(n) - 1 and a(n) + 1 are both terms of A028442.
%C Both A045882 and A028442 are infinite and this allows for the possibility that this sequence is also infinite (for A028442 see comment of A002321).
%F (A002321(a(n)) - A008683(a(n))) = (A002321(a(n)) + A008683(a(n+1))) = (A008683(a(n)) + A008683(a(n+1))) = 0.
%e 165 is a term because A002321(164) = A002321(166) = 0.
%e 237 is a term because A002321(236) = A002321(238) = 0.
%p with(numtheory): a:=n->add(mobius(k),k=1..n): select(n->a(n-1)=0 and a(n+1)=0,[$2..2200]); # _Muniru A Asiru_, Sep 20 2018
%t With[{s = Partition[Accumulate@ Array[MoebiusMu, 5300], 3, 1]}, 1 + First /@ Position[s, {0, k_, 0} /; k != 0]] (* _Michael De Vlieger_, Sep 24 2018 *)
%o (PARI) isok(n) = {if (n > 1, x = sum(k=1, n-1, moebius(k)); if (x == 0, if (x + moebius(n) + moebius(n+1) == 0, return (1)););); return (0);} \\ _Michel Marcus_, Sep 27 2018
%Y Cf. A002321, A008683, A028442, A045882.
%K nonn
%O 1,1
%A _Torlach Rush_, Sep 20 2018