

A083522


Smallest k such that k*(k+1)*(k+2)*...*(k+n1) + 1 is prime, or 0 if no such number exists.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 PocklingtonLehmer "P1" primality test is used, as implemented in PARI 2.1.3.


LINKS



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+n1, j)+1, 1), k++, b=1)); print1(if(k<m, k, 0), ", "))


CROSSREFS



KEYWORD

nonn


AUTHOR

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


EXTENSIONS



STATUS

approved



