Find the smallest positive integer k such that, for every positive integer n, 6n+k is relatively prime to each of 6n+3, 6n+2, and 6n+1.

a=1; b=0;c=gcd(6*a+1, 6*a+2, 6*a+3, 6*a+b); if(c==1, goto4, goto5);printc, a, b; a++;if(a<100, goto2, 0);a=1;b++;if(b<100, goto2, discard=0;

OUTPUT: It works for all k from k = 0 to infinity. So, the "smallest k = 0".