A173342 Numbers n such that n^7 and a cube are between consecutive squares.

2, 3, 498, 2266144, 272585923

Offset

1,1

Comments

No other terms < 10^8. The corresponding sequence for n^5 is A173341. Are there ever more than two perfect powers between consecutive squares?

a(6) > 10^10. [From Donovan Johnson, Apr 17 2010]

Links

Table of n, a(n) for n=1..5.

Example

2 is here because 2^7=128 and 5^3=125 are between 11^2=121 and 12^2=144.
3 is here because 3^7=2187 and 13^3=2197 are between 46^2=2116 and 47^2=2209.
498 is here because 498^7 and 1965781^3 are between 2756149047^2 and 2756149048^2.
2266144 is here because 2266144^7 and 674534510965903^3 are between 17518876914709436673663^2 and 17518876914709436673664^2.

Mathematica

t={}; Do[n2=Floor[n^(7/2)]; n3=Round[n^(7/3)]; If[n2^2<n3^3<(n2+1)^2 && n2^2<n^7<(n2+1)^2 && n3^3 != n^7, AppendTo[t, n]], {n, 10^4}]; t

Crossrefs

A097056, A117896

Sequence in context: A355644 A128874 A196070 * A090510 A348360 A004887

Adjacent sequences: A173339 A173340 A173341 * A173343 A173344 A173345

Keyword

nonn

Author

T. D. Noe, Feb 16 2010

Extensions

a(5) from Donovan Johnson, Apr 17 2010

Status

approved