Cube of 71 is Odd Integers in Sequence
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Theorem
The cube of $71$, when expressed in decimal notation, is the odd integers from $3$ to $11$ written in sequence:
- $71^3 = 357 \, 911$
Proof
Verified by direct calculation.
Historical Note
The interesting phenomenon that $71^3$ consists of the odd integers from $3$ to $11$ in sequence is reported by David Wells in Curious and Interesting Numbers as being noted by a contributor to Journal of Recreational Mathematics called James Davies, writing in Volume $13$.
An online listing of the articles for that journal has revealed an article titled An Evening With Pi by James Davis, but further investigation will need to be done to establish the exact nature of this.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $71$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $71$