%I #6 Oct 16 2024 21:40:10
%S 3,-2,5,-6,7,-10,9,-20,11,-30,13,-46,15,-56,17,-84,19,-88,21,-116,23,
%T -126,25,-154,27,-164,29,-168,31,-196,33,-206,35,-234,37,-244,39,-272,
%U 41,-306,43,-376,45,-386,47,-414,49,-472,51,-518,53,-546,55,-562,57,-584,59,-600,61,-748
%N Alternating sum of twin primes (A001097).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>.
%F a(n) = Sum_{k=1..n} (-1)^(k+1) * A001097(k).
%F a(2*n-1) = 2*n+1.
%Y Cf. A001097, A008347, A048598.
%K sign,new
%O 1,1
%A _Ilya Gutkovskiy_, Oct 08 2024