A173341 Numbers n such that n^5 and a cube are between consecutive squares.

2, 23, 199, 201, 408, 575, 603, 1354, 1628, 4995, 5745, 7320, 7994, 12634, 42637, 44217, 45962, 67132, 82131, 82351, 91116, 91134, 146521, 177682, 229863, 359373, 394826, 458908, 462763, 512012, 665719, 728982, 1009965, 1156978, 1450803

Offset: 1

Author

T. D. Noe, Feb 16 2010

Keywords

• nonn

Comments

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?

Examples

			2 is here because 2^5=32 and 3^3=27 are between 5^2=25 and 6^2=36.
23 is here because 23^5 and 186^3 are between 2536^2 and 2537^2.
199 is here because 199^5 and 6783^3 are between 558640^2 and 558641^2.
		

Crossrefs

A097056, A117896

Programs

Mathematica

t={}; Do[n2=Floor[n^(5/2)]; n3=Round[n^(5/3)]; If[n2^2