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 A376890 #11 Nov 09 2024 06:38:29
%S A376890 3,-2,5,-6,7,-10,9,-20,11,-30,13,-46,15,-56,17,-84,19,-88,21,-116,23,
%T A376890 -126,25,-154,27,-164,29,-168,31,-196,33,-206,35,-234,37,-244,39,-272,
%U A376890 41,-306,43,-376,45,-386,47,-414,49,-472,51,-518,53,-546,55,-562,57,-584,59,-600,61,-748
%N A376890 Alternating sum of twin primes (A001097).
%H A376890 Robert Israel, <a href="/A376890/b376890.txt">Table of n, a(n) for n = 1..10000</a>
%H A376890 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>.
%F A376890 a(n) = Sum_{k=1..n} (-1)^(k+1) * A001097(k).
%F A376890 a(2*n-1) = 2*n+1.
%p A376890 T1:= select(t -> isprime(t) and isprime(t+2), [seq(i,i=5..1000,6)]):
%p A376890 T:= map(t -> (-t, t+2), T1): T:= [3,op(T)]:
%p A376890 ListTools:-PartialSums(T); # _Robert Israel_, Nov 08 2024
%Y A376890 Cf. A001097, A008347, A048598.
%K A376890 sign
%O A376890 1,1
%A A376890 _Ilya Gutkovskiy_, Oct 08 2024