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%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
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