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

1,1

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?

Links

Table of n, a(n) for n=1..35.

Example

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.

Mathematica

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

Crossrefs

A097056, A117896

Sequence in context: A352355 A200846 A198851 * A118756 A133955 A062600

Adjacent sequences: A173338 A173339 A173340 * A173342 A173343 A173344

Keyword

nonn

Author

T. D. Noe, Feb 16 2010

Status

approved