This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117594 #11 Aug 09 2025 22:35:37
%S A117594 199,1354,4995,7320,7994,12634,44217,91116,177682,394826,458908,
%T A117594 462763,512012,1706886,1738064,1801677,1880465,2523441,5691648,
%U A117594 6714911,8383950,8403388,11100341,14706104,14706146,15460136,16337238,18898872,21194961
%N A117594 Numbers whose fifth powers are closer to cubic numbers than square numbers.
%C A117594 Numbers which are cubes themselves are excluded as trivial.
%C A117594 It appears that this sequence is infinite. For seventh powers < 10^49, only 2^7 and 3^7 are closer to cubes than squares. Note that 1/2+1/3+1/5>1, but 1/2+1/3+1/7<1. Do these inequalities determine whether there are an infinite or finite number of solutions? Mazur discusses how the ABC conjecture applies to perfect power problems. - _T. D. Noe_, Apr 07 2006
%H A117594 B. Mazur, <a href="http://www.math.harvard.edu/~mazur/papers/scanQuest.pdf">Questions about Number</a>
%H A117594 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPower.html">MathWorld: Perfect Power</a>
%e A117594 The distance of 199^5 to the nearest cube is 49688. To the nearest square is 165882.
%t A117594 nMax=10^5; lst={}; Do[n5=n^5; n3=Round[n5^(1/3)]^3; n2=Round[n5^(1/2)]^2; If[0 < Abs[n5-n3] < Abs[n5-n2], AppendTo[lst,n]], {n,nMax}]; lst (* _T. D. Noe_, Apr 07 2006 *)
%Y A117594 Cf. A117934 (perfect powers that are close).
%K A117594 nonn
%O A117594 1,1
%A A117594 _Ed Pegg Jr_, Apr 05 2006
%E A117594 More terms from _T. D. Noe_ and _Hans Havermann_, Apr 08 2006