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.
%I A071532 #14 Jul 23 2024 21:45:19
%S A071532 1,0,1,2,3,4,5,6,5,6,5,6,5,6,7,6,7,8,7,8,9,10,9,8,9,8,9,8,7,8,7,8,9,
%T A071532 10,11,10,9,10,9,8,7,8,7,6,7,8,7,8,7,6,5,6,7,6,7,6,7,8,9,8,9,10,11,12,
%U A071532 13,12,11,10,11,10,11,10,9,10,9,10,9,8,7,6,5,6,7,6,7,6,5,4,5,6,5,4,5,4,3
%N A071532 a(n) = (-1) * Sum_{k=1..n} (-1)^floor((3/2)^k).
%C A071532 Let b(n) denote the number of k with 0<=k<=n such that floor((3/2)^k) = A002379(k) is even; then a(n) = n-2*b(n).
%C A071532 Equivalently: let c(n) denote the number of k, 0<=k<=n, such that floor((3/2)^k) = A002379(k) is odd, then a(n) = 2*c(n)-n.
%C A071532 Is a(n)>0? For n large enough does a(n)>sqrt(n) always hold?
%C A071532 Conjecture: asymptotically, a(n) ~ C * Log(n)^2 with C = 1.4.....
%H A071532 Robert G. Wilson v, <a href="/A071532/a071532.jpg">Graph of first 100000 terms</a>
%F A071532 a(n) = (-1) * Sum_{i=1..n} (-1)^A002379(i).
%t A071532 a[0] = 0; a[n_] := a[n] = a[n - 1] - (-1)^Floor[(3/2)^n]; Table[ a[n], {n, 0, 95}]
%o A071532 (PARI) a(n)=-sum(i=1, n, sign((-1)^floor((3/2)^i)))
%o A071532 (PARI) a(n)=n-2*sum(k=0,n,if(floor((3/2)^k)%2,0,1))
%Y A071532 Cf. A002379, A072418.
%K A071532 easy,nonn
%O A071532 1,4
%A A071532 _Benoit Cloitre_, Jun 20 2002
%E A071532 Edited by _Ralf Stephan_, Sep 01 2004