31 lines
1.3 KiB
Text
31 lines
1.3 KiB
Text
do -- find some Humble numbers - numbers with no prime factors above 7
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local maxHumble <const>, maxShownHumble <const> = 2048, 50
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local h, hCount = {}, { [0] = 0, 0, 0, 0, 0, 0, 0 }
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local p2, p3, p5, p7 = 2, 3, 5, 7
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local last2, last3, last5, last7 = 1, 1, 1, 1
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-- 1 is the first humble number ( 2^0 * 3^0 * 5^0 * 7^0 ) and has 1 digit
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h[ 1 ], hCount[ 1 ] = 1, 1
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io.write( "1" )
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for n = 2, maxHumble do
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-- the next humble number is the lowest of the next multiples of 2, 3, 5, 7
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local m = math.min( p2, p3, p5, p7 )
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h[ n ] = m
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if n <= maxShownHumble then io.write( " ", m ) end
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if m == p2 then last2 += 1 p2 = 2 * h[ last2 ] end
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if m == p3 then last3 += 1 p3 = 3 * h[ last3 ] end
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if m == p5 then last5 += 1 p5 = 5 * h[ last5 ] end
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if m == p7 then last7 += 1 p7 = 7 * h[ last7 ] end
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hCount[ ( m < 10 ) ? 1
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: ( m < 100 ) ? 2
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: ( m < 1_000 ) ? 3
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: ( m < 10_000 ) ? 4
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: ( m < 100_000 ) ? 5
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: ( m < 1_000_000 ) ? 6
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: 0
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] += 1
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end
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io.write( "\n" )
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for i = 1, 6 do
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io.write( string.format( "There are %4d Humble numbers with %d digits\n", hCount[ i ], i ) )
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end
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end
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