cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A349229 #12 Nov 13 2021 02:32:41
%S A349229 -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,
%T A349229 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,
%U A349229 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
%N A349229 a(n) = Sum_{k=1..n} (-1)^A001222(k)*(-1)^A001222(k+1).
%C A349229 It is conjectured that a(n)=o(n).
%H A349229 Kaisa Matomäki, Maksym Radziwiłł and Terence Tao, <a href="http://dx.doi.org/10.2140/ant.2015.9.2167">An averaged form of Chowla's conjecture</a>, Algebra & Number Theory, Vol. 9, No. 9 (2015), pp. 2167-2196.
%t A349229 a[n_] := Sum[(-1)^(PrimeOmega[k] + PrimeOmega[k + 1]), {k, 1, n}]; Array[a, 100] (* _Amiram Eldar_, Nov 11 2021 *)
%o A349229 (PARI) a(n)=sum(k=1,n,(-1)^bigomega(k)*(-1)^bigomega(k+1))
%Y A349229 Cf. A001222.
%K A349229 sign
%O A349229 1,4
%A A349229 _Benoit Cloitre_, Nov 11 2021