A173341 - OEIS

%I #2 Mar 30 2012 17:22:55

%S 2,23,199,201,408,575,603,1354,1628,4995,5745,7320,7994,12634,42637,

%T 44217,45962,67132,82131,82351,91116,91134,146521,177682,229863,

%U 359373,394826,458908,462763,512012,665719,728982,1009965,1156978,1450803

%N Numbers n such that n^5 and a cube are between consecutive squares.

%C This sequence appears to be infinite. Sequence A117594 is a subsequence. The corresponding sequence for n^7 is A173342. Are there ever more than two perfect powers between consecutive squares?

%e 2 is here because 2^5=32 and 3^3=27 are between 5^2=25 and 6^2=36.

%e 23 is here because 23^5 and 186^3 are between 2536^2 and 2537^2.

%e 199 is here because 199^5 and 6783^3 are between 558640^2 and 558641^2.

%t t={}; Do[n2=Floor[n^(5/2)]; n3=Round[n^(5/3)]; If[n2^2<n3^3<(n2+1)^2 && n2^2<n^5<(n2+1)^2 && n3^3 != n^5, AppendTo[t,n]], {n,10^4}]; t

%Y A097056, A117896

%K nonn

%O 1,1

%A _T. D. Noe_, Feb 16 2010