Problem 29
Statement
Consider all integer combinations of a for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
2²=4, 2³=8, 2⁴=16, 2⁵=32
3²=9, 3³=27, 3⁴=81, 3⁵=243
4²=16, 4³=64, 4⁴=256, 4⁵=1024
5²=25, 5³=125, 5⁴=625, 5⁵=3125
If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
Solution
class SquareSequence
def initialize(max)
@sequence = []
@min = 2
@max = max
(@min..@max).each do |i|
seq = []
(@min..@max).each do |j|
seq << i**j
end
@sequence = @sequence | seq
end
end
def length
return @sequence.length
end
end
seq = SquareSequence.new(100)
puts seq.length
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