%I #11 Apr 04 2012 12:13:37
%S 17,145,1095,8098,59868,442406,3269011
%N Least k such that log(ceiling(sqrt(k!))^2-k!)/k > n.
%C This sequence show how quickly A068869 increase in a logarithmic scale.
%e a(1)=17 because log(ceiling(sqrt(17!))^2-17!)/17 = 1.00471 > 1.
%t kkk = 0; n = 1; Do[While[kkk < max, n++; kk = Floor[Sqrt[n!]]; kkk = N[Log[(kk + 1)^2 - n!]/n]]; Print[n], {max, 1, 5}]
%o (PARI) a(n)=my(k=solve(x=1,4<<(3*n),(log(2)+lngamma(x+1)/2)/x-n)\1,f=k!);while(n>log((sqrtint(f*=k++)+1)^2-f)/k,);k \\ _Charles R Greathouse IV_, Apr 03 2012
%Y Cf. A068869.
%K nonn,hard,more
%O 1,1
%A _Artur Jasinski_, Apr 01 2012
%E a(6)-a(7) from _Charles R Greathouse IV_, Apr 03 2012