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%I #12 May 25 2018 00:53:46
%S 0,2,1,10,17,6,1,18,209,62,255,288,9,510,341,132,95,564,737,734,1243,
%T 1222,427,1022,425,1630,649,1836,311,2582,571,2816,3083,2768,1221,
%U 4142,1835,994,3695,1338,1337,1576,885,3522,2221,1222,4897,5340,3641,1988,8791,5410,843,10658,5083,2082
%N The difference prime(i)+prime(i+1)+...+prime(i+n-1)-A002110(n), where prime(i) is the smallest prime such that the value is nonnegative.
%C It is an open problem whether there is n>1 (necessarily even) such that a(n)=0.
%C If A196129(n)=0, then also a(n)=0 and the prime p[i] is given by A196128(n); else it is the next larger prime.
%H J. M. Bergot, C. Rivera (Ed.), <a href="http://www.primepuzzles.net/problems/prob_056.htm">Problem 56. p1*p2*...*pk = q1+q2+...+qk</a>, on primepuzzle.net.
%o (PARI) A196130(k)={ my( P=A002110(k), p=precprime(P\k), q=p, S=p);
%o for(n=1, k, S+=if(S*k>P*n, p=precprime(p-1), q=nextprime(q+1))); if(S-q-P,S-p-P)}
%Y Cf. A196128, A196129.
%K nonn
%O 1,2
%A _M. F. Hasler_, Sep 28 2011
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