The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319502 Indices of Mertens's function M(n) (A002321) whose nearest neighbors have value 0. 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 (list; graph; refs; listen; history; text; internal format)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 11:59 EST 2021. Contains 349440 sequences. (Running on oeis4.)