Giorgos Kalogeropouls sent the following nice puzzle:
Cube Root Smooth (CRS) numbers are numbers k whose
largest prime factor lpf(k) <= k^(1/3) (
A090081)
In this challenge you are asked to find the least
number k that produces a run of exactly n
consecutive CRS numbers.
n=1 -> 8
n=2 -> 2400, 2401
n=3 -> 134848,
134849, 134850
n=4 -> 3678723, 3678724, 3678725,
3678726
Example:
n=2
- 2400 = 25 × 3 × 52
& 5^3 = 125< 2400
- 2401 = 74 & 7^3 = 343 < 2401
Q1: Find the least k that starts a run of
5,6,7... consecutive CRS numbers.
Q2: Is this sequence infinite?
Q3: What is the longest run of consecutive
CRS numbers that you can find?
