No More

[N. J. A. Sloane]

actually i added that keyword "more" the last time
i edited that sequence

the reason is that it looks like this:

%I A038698
%S A038698 0,1,0,1,2,1,0,1,2,1,2,1,0,1,2,1,2,1,2,3,2,3,4,3,2,1,2,3,2,1,2,3,2,3,2,
%T A038698 3,2,3,4,3,4,3,4,3,2,3,4,5,6,5,4,5,4,5,4,5,4,5,4,3,4,3,4,5,4,3,4,3,4,3,
%U A038698 2,3,4,3,4,5,4,3,2,1
%N A038698 Surfeit of 4k-1 primes over 4k+1 primes, beginning with prime 2.
%C A038698 a(n)<0 for infinitely many values of n - Benoit Cloitre (abcloitre at wanadoo.fr), Jun 24 2002
%D A038698 Stan Wagon, The Power of Visualization, Front Range Press, 1994, p. 2.
%F A038698 FoldList[ Plus,0,Mod[ Prime[ Range[ 2,80 ] ],4 ]-2 ]
%F A038698 a(n) = sum(k=2,n,(-1)^((prime(n)+1)/2)) - Benoit Cloitre (abcloitre at wanadoo.fr), Jun 24 2002
%o A038698 (PARI) for(n=2,100,print1(sum(i=2,n,(-1)^((prime(i)+1)/2)),","))
%Y A038698 Cf. A007350, A007351, A038691, A066520.
%K A038698 nonn,easy,more
%O A038698 1,5
%A A038698 Hans Havermann (hahaj at rogers.com)

There's room for further terms to complete the third line, and it would
be easy to compute them.

Neil

PS Yes, the same is true for many other sequences, agreed!