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EXAMPLE
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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.
a(4) = 10199373: r = 10199373, s = 7247646. - William Rex Marshall, Nov 23 2009
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PROG
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(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]
a(n)=my(r=n); while(!is(r++, n), ); r \\ Charles R Greathouse IV, Nov 05 2013
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EXTENSIONS
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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.
a(4) > 1475000. - Jud McCranie, Jan 26 2000
a(4) from William Rex Marshall, Nov 23 2009
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