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A233809 a(n) = Sum_{k=1..n} prime(k) * s(k), where s(k) = (-1)^(floor(k/2)).

%I A233809 #24 Sep 08 2022 08:46:06
%S A233809 2,-1,-6,1,12,-1,-18,1,24,-5,-36,1,42,-1,-48,5,64,3,-64,7,80,1,-82,7,
%T A233809 104,3,-100,7,116,3,-124,7,144,5,-144,7,164,1,-166,7,186,5,-186,7,204,
%U A233809 5,-206,17,244,15,-218,21,262,11,-246,17,286,15,-262
%N A233809 a(n) = Sum_{k=1..n} prime(k) * s(k), where s(k) = (-1)^(floor(k/2)).
%C A233809 s(k) starts +1, -1, -1, +1, +1, -1, -1, ...
%H A233809 Vincenzo Librandi, <a href="/A233809/b233809.txt">Table of n, a(n) for n = 1..2000</a>
%e A233809 a(6) = +2 - 3 - 5 + 7 + 11 - 13 = -1.
%t A233809 f[n_] := Sum[(-1)^Floor[k/2]*Prime[k], {k, n}]; Array[f, 60] (* _Robert G. Wilson v_, Aug 06 2017 *)
%o A233809 (PARI)
%o A233809 s(k) = (-1)^(floor(k/2));
%o A233809 a(n) = sum(k=1,n,s(k)*prime(k));
%o A233809 \\ _Joerg Arndt_, Aug 06 2017
%o A233809 (Magma) [&+[NthPrime(k)*(-1)^(Floor(k/2)): k in [1..n]]: n in [1..60]]; // _Vincenzo Librandi_, Aug 07 2017
%Y A233809 Cf. A008347, A233399.
%Y A233809 Cf. A130642 (a(n) = -1), A130643 (a(n) = 1). - _Michel Marcus_, Aug 06 2017
%K A233809 sign,easy,less
%O A233809 1,1
%A A233809 _Jon Perry_, Dec 16 2013
%E A233809 Name corrected by _Joerg Arndt_, Aug 06 2017