A349229 a(n) = Sum_{k=1..n} (-1)^A001222(k)*(-1)^A001222(k+1).

-1, 0, -1, -2, -3, -4, -3, -4, -3, -4, -3, -2, -3, -2, -1, -2, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 6, 5, 6, 7, 6, 7, 8, 9, 10, 9, 8, 9, 8, 7, 6, 5, 6, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 4, 3, 4, 5, 4, 3, 4, 5, 6, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 6, 7, 6, 5, 6, 5, 4, 5, 6, 7, 6, 7, 8, 7, 6

Offset: 1

Author

Benoit Cloitre, Nov 11 2021

Keywords

• sign

Comments

It is conjectured that a(n)=o(n).

Links

• Kaisa Matomäki, Maksym Radziwiłł and Terence Tao, An averaged form of Chowla's conjecture, Algebra & Number Theory, Vol. 9, No. 9 (2015), pp. 2167-2196.

Crossrefs

Cf. A001222.

Programs

Mathematica

a[n_] := Sum[(-1)^(PrimeOmega[k] + PrimeOmega[k + 1]), {k, 1, n}]; Array[a, 100] (* Amiram Eldar, Nov 11 2021 *)

PARI

a(n)=sum(k=1,n,(-1)^bigomega(k)*(-1)^bigomega(k+1))