A221280 Numbers m such that lambda(m) = lambda(m+1), where lambda(n) = A008836(n) is the Liouville function.

2, 7, 9, 11, 12, 14, 15, 17, 18, 19, 21, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 38, 39, 41, 42, 43, 44, 47, 52, 54, 55, 56, 57, 64, 66, 67, 70, 71, 72, 75, 78, 79, 81, 84, 85, 86, 87, 90, 93, 94, 95, 97, 98, 101, 102, 107, 108, 109, 112, 113, 116, 118, 121, 122, 124, 127, 130

Offset

1,1

Comments

Sequence is infinite. Density is conjecturally 1/2; it is easy to show that the density is at least 1/4 (one of k, 2k, and 2k+1 is in this sequence).

m is a term iff lambda(A000217(m)) = -1. See link. - Jon Maiga, Jan 03 2019

Links

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

J. Maiga, Liouville's function and triangular numbers, 2018.

Mathematica

Select[ Range[130], LiouvilleLambda[#] == LiouvilleLambda[# + 1] &] (* Jean-François Alcover, Jul 30 2013 *)

Prog

(PARI) is(n)=(-1)^bigomega(n)==(-1)^bigomega(n+1)

Crossrefs

Cf. A000217, A008836, A221281, A221282.

Sequence in context: A073074 A034796 A047526 * A166570 A003668 A191263

Adjacent sequences: A221277 A221278 A221279 * A221281 A221282 A221283

Keyword

nonn

Author

Charles R Greathouse IV, Jan 09 2013

Status

approved