A083522 Smallest k such that k*(k+1)*(k+2)*...*(k+n-1) + 1 is prime, or 0 if no such number exists.

1, 1, 1, 0, 3, 3, 4, 4, 6, 2, 1, 10, 5, 3, 9, 6, 6, 4, 5, 8, 6, 7, 19, 25, 11, 2, 1, 3, 9, 23, 7, 7, 39, 5, 7, 2, 1, 5, 78, 2, 1, 15, 19, 12, 17, 6, 3, 14, 8, 21, 23, 17, 14, 40, 16, 6, 8, 13, 15, 5, 15, 82, 46, 51, 39, 43, 6, 11, 61, 57, 16, 2, 1, 26, 54, 2, 1, 13, 4, 62, 31, 69, 27, 155, 21

Offset

1,5

Comments

The product of four consecutive integers + 1 is always composite (a square), so a(4) = 0. Are there any more zeros in the sequence?

Since rather large numbers (up to 193 digits) are encountered in the computation, the Pocklington-Lehmer "P-1" primality test is used, as implemented in PARI 2.1.3.

Links

Table of n, a(n) for n=1..85.

Example

1*2*3*4*5 + 1 = 121 = 11*11 and 2*3*4*5*6 + 1 = 721 = 7*103 are composite, but 3*4*5*6*7 + 1 = 2521 is prime, so a(5) = 3.

Prog

(PARI) m=1000; for(n=1, 85, b=0; k=1; while(b<1&&k<m, if(!isprime(prod(j=k, k+n-1, j)+1, 1), k++, b=1)); print1(if(k<m, k, 0), ", "))

Crossrefs

Cf. A083520, A083521.

Sequence in context: A369217 A369218 A097356 * A355067 A108942 A025561

Adjacent sequences: A083519 A083520 A083521 * A083523 A083524 A083525

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003

Extensions

Edited and extended by Klaus Brockhaus and Don Reble, May 06 2003

Status

approved