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 A378677 #16 Dec 06 2024 16:30:20
%S A378677 0,3,8,-8,-3,14,-14,17,-17,24,-24,35,-35,32,-32,51,-51,58,-58,69,-69,
%T A378677 88,-88,91,-91,100,-100,111,-111,130,-130,147,-147,136,-136,195,-195,
%U A378677 158,-158,209,-209,192,-192,239,-239,222,-222,287,-287,260,-260,303,-303
%N A378677 a(n)=a(n-1) + prime(n) for n prime, and a(n)=-a(n-1) otherwise, with a(0)=0, with duplicates removed afterwards.
%C A378677 Let b = subset of positive terms for n>4. We have A073131= b(m+2)-b(m) , A006450= b(m+2)+b(m) and A299644= b(m+2)+2*b(m+1)+b(m).
%H A378677 Paolo Xausa, <a href="/A378677/b378677.txt">Table of n, a(n) for n = 0..10000</a>
%F A378677 a(n) = a(n-1) + a prime for n odd >4.
%F A378677 a(n) = -a(n-1) for a(n-1)>0, n>1.
%e A378677 n=1 is not prime, so a(1)= -a(0)= 0. n=2 is prime, so a(2)=a(1)+prime(2)=0+3=3. n=5 is prime, so a(5)=3, but note that it duplicates a(2). n=6 is not prime, so a(6)= -a(5)=-3. After terms are computed, duplicates are only then removed, which will alter indices accordingly.
%t A378677 Module[{n = 0}, DeleteDuplicates[NestList[If[PrimeQ[++n], # + Prime[n], -#] &, 0, 200]]] (* _Paolo Xausa_, Dec 06 2024 *)
%Y A378677 Cf. A006450, A073131, A299644.
%K A378677 sign
%O A378677 0,2
%A A378677 _Bill McEachen_, Dec 03 2024