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%I #25 Jun 09 2018 10:32:29
%S 2,21,1310,10199373
%N Least positive integer r such that there exists an integer s, 0 <= s < r gcd(r-i, s-j) > 1 for all integers i, j with 0 <= i, j < n.
%H S. Laishram, F. Luca, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Laishram/lai2.html">Rectangles Of Nonvisible Lattice Points</a>, J. Int. Seq. 18 (2015) 15.10.8
%F a_n < e^{(1+o(1)) 2 n^2 log n}.
%e a(1) = 2 because we can choose r = 2, s = 0; a(2) = 21 because we can choose r = 21, s = 15; a(3) = 1310 because we can choose r = 1310, s = 1276.
%e a(4) = 10199373: r = 10199373, s = 7247646. - _William Rex Marshall_, Nov 23 2009
%o (PARI) is(r,n)=n--;my(s=[Mod(0,1)],f,v,p);for(i=0,n,f=factor(r-i)[,1]; for(j=0,n, v=List(); for(k=1,#f, p=f[k]; for(k=1,#s, if(s[k].mod%p, listput(v,chinese(Mod(j,p),s[k])), if(Mod(s[k],p)==j, listput(v,s[k]))))); s=select(m->lift(m)<r,Set(v)); if(#s==0, return(0)))); s[1]
%o a(n)=my(r=n); while(!is(r++,n),); r \\ _Charles R Greathouse IV_, Nov 05 2013
%K nonn,nice,more
%O 1,1
%A _Jeffrey Shallit_, Jan 25 2000
%E By brute force search I know that a(4) > 410000. And also I know by constructing the pair (r, s) = (477742707, 172379781) that a(4) <= 477742707.
%E a(4) > 1475000. - _Jud McCranie_, Jan 26 2000
%E a(4) from _William Rex Marshall_, Nov 23 2009
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