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A349229
a(n) = Sum_{k=1..n} (-1)^A001222(k)*(-1)^A001222(k+1).
0
-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
1,4
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.
MATHEMATICA
a[n_] := Sum[(-1)^(PrimeOmega[k] + PrimeOmega[k + 1]), {k, 1, n}]; Array[a, 100] (* Amiram Eldar, Nov 11 2021 *)
PROG
(PARI) a(n)=sum(k=1, n, (-1)^bigomega(k)*(-1)^bigomega(k+1))
CROSSREFS
Cf. A001222.
Sequence in context: A139048 A182101 A242289 * A158515 A285884 A123709
KEYWORD
sign
AUTHOR
Benoit Cloitre, Nov 11 2021
STATUS
approved