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A305299 a(0) = 0, a(1) = 1, a(2) = 2; for n >= 2, a(2*n-1) = n - 2*a(n-1) - 1, a(2*n) = a(2*n-1) - a(n).

%I A305299 #14 Sep 12 2018 02:12:20
%S A305299 0,1,2,-1,-3,-2,-1,5,8,10,12,9,10,8,3,-3,-11,-8,-18,-11,-23,-14,-23,
%T A305299 -7,-17,-8,-16,-3,-6,8,11,21,32,38,46,33,51,54,65,41,64,66,80,49,72,
%U A305299 68,75,37,54,58,66,41,57,58,61,33,39,40,32,13,2,8,-13,-11,-43,-32,-70,-43,-89,-58,-91,-31,-82,-66,-120,-71,-136,-92
%N A305299 a(0) = 0, a(1) = 1, a(2) = 2; for n >= 2, a(2*n-1) = n - 2*a(n-1) - 1, a(2*n) = a(2*n-1) - a(n).
%C A305299 This sequence has an approximate self-similar block structure, which is roughly described by A110286, see Links section.
%C A305299 a(0) = 0 by definition. The next 0 is a(970) = 0. What are the other numbers k such that a(k) = 0?
%H A305299 Robert Israel, <a href="/A305299/b305299.txt">Table of n, a(n) for n = 0..10000</a>
%H A305299 Rémy Sigrist, <a href="/A305299/a305299.png">Density plot of the first 16000000 terms</a>
%H A305299 Altug Alkan, <a href="/A305299/a305299_1.png">A scatterplot of a(n) for n <= 15*2^12</a>
%H A305299 Altug Alkan, <a href="/A305299/a305299_2.png">A scatterplot of a(n) for 15*2^12 <= n <= 15*2^14</a>
%p A305299 f:= proc(n) option remember;
%p A305299   if n::odd then (n-1)/2-2*procname((n-1)/2)
%p A305299   else procname(n-1)-procname(n/2)
%p A305299   fi
%p A305299 end proc:
%p A305299 f(0):= 0: f(1):= 1: f(2):= 2:
%p A305299 map(f, [$0..77]); # after _Robert Israel_ at A294044
%t A305299 a[0] = 0; a[1] = 1; a[2] = 2; a[n_] := If[EvenQ[n], a[n - 1] - a[n/2],  (n - 1)/2 - 2 a[(n - 1)/2]]; Table[a[n], {n, 0, 77}] (* after _Ilya Gutkovskiy_ at A294044 *)
%o A305299 (PARI) a(n)=if(n<=2, n, if(n%2==1, (n-1)/2-2*a((n-1)/2), a(n-1)-a(n/2)));
%o A305299 (PARI) a = vector(77); print1 (0", "); for (k=1, #a, print1 (a[k]=if (k<=2, k, my (n=k\2); if (k%2==0, a[2*n-1]-a[n], n-2*a[n]))", ")) \\ after _Rémy Sigrist_ at A303028
%Y A305299 Cf. A002487, A294044, A303028.
%K A305299 sign,look
%O A305299 0,3
%A A305299 _Altug Alkan_, Aug 18 2018