A221281 Numbers n such that lambda(n) = lambda(n+1) = lambda(n+2), where lambda(n) = A008836(n) is the Liouville function.

11, 14, 17, 18, 24, 27, 28, 29, 30, 33, 34, 38, 41, 42, 43, 54, 55, 56, 66, 70, 71, 78, 84, 85, 86, 93, 94, 97, 101, 107, 108, 112, 121, 132, 133, 134, 137, 140, 141, 142, 143, 144, 147, 158, 159, 162, 163, 170, 171, 172, 173, 174, 179, 180, 183, 190, 191, 201, 202, 203, 204

Offset

1,1

Comments

Hildebrand proved that this sequence is infinite. More generally, he showed that the eight values (1, 1, 1), (1, 1, -1), ..., (-1, -1, -1) each appear infinitely often as consecutive values of the Liouville function.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Adolf Hildebrand, On consecutive values of the Liouville function, Enseign. Math. (2) 32 (1986), no. 3-4, pp. 219-226.

Mathematica

SequencePosition[LiouvilleLambda[Range[250]], {x_, x_, x_}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 16 2021 *)

Prog

(PARI) is(n)=my(k=(-1)^bigomega(n)); k==(-1)^bigomega(n+1) && k==(-1)^bigomega(n+2)

Crossrefs

Subsequence of A221280. Cf. A008836, A221282.

Sequence in context: A038630 A239935 A219179 * A025058 A025060 A093669

Adjacent sequences: A221278 A221279 A221280 * A221282 A221283 A221284

Keyword

nonn

Author

Charles R Greathouse IV, Jan 09 2013

Status

approved