A196130 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.

0, 2, 1, 10, 17, 6, 1, 18, 209, 62, 255, 288, 9, 510, 341, 132, 95, 564, 737, 734, 1243, 1222, 427, 1022, 425, 1630, 649, 1836, 311, 2582, 571, 2816, 3083, 2768, 1221, 4142, 1835, 994, 3695, 1338, 1337, 1576, 885, 3522, 2221, 1222, 4897, 5340, 3641, 1988, 8791, 5410, 843, 10658, 5083, 2082

Offset

1,2

Comments

It is an open problem whether there is n>1 (necessarily even) such that a(n)=0.

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.

Links

Table of n, a(n) for n=1..56.

J. M. Bergot, C. Rivera (Ed.), Problem 56.  p1*p2*...*pk = q1+q2+...+qk, on primepuzzle.net.

Prog

(PARI) A196130(k)={ my( P=A002110(k), p=precprime(P\k), q=p, S=p);
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)}

Crossrefs

Cf. A196128, A196129.

Sequence in context: A151363 A213303 A213304 * A177439 A290597 A136205

Adjacent sequences: A196127 A196128 A196129 * A196131 A196132 A196133

Keyword

nonn

Author

M. F. Hasler, Sep 28 2011

Status

approved