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A173342 Numbers n such that n^7 and a cube are between consecutive squares. 3
2, 3, 498, 2266144, 272585923 (list; graph; refs; listen; history; text; internal format)
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: A306370 A128874 A196070 * A090510 A004887 A240709

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

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Last modified July 27 02:39 EDT 2021. Contains 346302 sequences. (Running on oeis4.)