A319502 Indices of Mertens's function M(n) (A002321) whose nearest neighbors have value 0.

165, 237, 330, 354, 357, 365, 402, 406, 421, 426, 794, 797, 813, 885, 894, 897, 905, 914, 1257, 1281, 1290, 1298, 1301, 1337, 1522, 1526, 1545, 1842, 1865, 2094, 2098, 2118, 2121, 2137, 4602, 4609, 4621, 4629, 4726, 4729, 4738, 5106, 5109, 5198, 5206, 5221

Offset

1,1

Comments

This sequence records the shortest intervals where M(n) leaves 0 before returning to 0.

a(n) - 1 and a(n) + 1 are both terms of A028442.

Both A045882 and A028442 are infinite and this allows for the possibility that this sequence is also infinite (for A028442 see comment of A002321).

Links

Table of n, a(n) for n=1..46.

Formula

(A002321(a(n)) - A008683(a(n))) = (A002321(a(n)) + A008683(a(n+1))) = (A008683(a(n)) + A008683(a(n+1))) = 0.

Example

165 is a term because A002321(164) = A002321(166) = 0.
237 is a term because A002321(236) = A002321(238) = 0.

Maple

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

Mathematica

With[{s = Partition[Accumulate@ Array[MoebiusMu, 5300], 3, 1]}, 1 + First /@ Position[s, {0, k_, 0} /; k != 0]] (* Michael De Vlieger, Sep 24 2018 *)

Prog

(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

Crossrefs

Cf. A002321, A008683, A028442, A045882.

Sequence in context: A168355 A083255 A259283 * A270175 A319328 A301970

Adjacent sequences: A319499 A319500 A319501 * A319503 A319504 A319505

Keyword

nonn

Author

Torlach Rush, Sep 20 2018

Status

approved