A196129 A002110(n)-(p[i]+p[i+1]+...+p[i+n-1]), where p[i] is the largest prime such that this is nonnegative.

0, 1, 7, 8, 13, 28, 51, 72, 31, 124, 3, 78, 331, 226, 119, 514, 517, 120, 85, 108, 423, 176, 1163, 830, 1935, 700, 2133, 1104, 1903, 730, 1811, 1318, 703, 1058, 3063, 344, 2337, 5816, 1945, 4162, 5801, 5498, 6337, 3998, 4501, 7376, 3617, 5430, 6891, 8786, 155, 4660, 8523, 790, 6203, 9742, 11389, 10792, 793

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..59.

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

Mathematica

a[n_] := (primorial = Product[Prime[k], {k, 1, n}]; s = NextPrime[Quotient[primorial, n], -1]; p = s; q = s; For[k = 1, k <= n, k++, s += If[s*n > primorial*k, p = NextPrime[p - 1, -1], q = NextPrime[q + 1]]]; primorial - s + q); a[1] = 0; a[2] = 1; Table[a[n], {n, 1, 59}] (* Jean-François Alcover, Jun 11 2013, translated and adapted from Pari *)

Prog

(PARI) A196129(k)={my(P=A002110(k), S=precprime(P\k), p=S, q=S); for(n=1, k, S+=if(S*k>P*n, p=precprime(p-1), q=nextprime(q+1))); P-S+q}

Crossrefs

The primes p[i] are given in A196128.

Sequence in context: A045765 A118068 A060754 * A286261 A136037 A085334

Adjacent sequences: A196126 A196127 A196128 * A196130 A196131 A196132

Keyword

nonn

Author

M. F. Hasler, Sep 28 2011

Status

approved