28 lines
1.5 KiB
Plaintext
28 lines
1.5 KiB
Plaintext
'''[[wp:Hamming numbers|Hamming numbers]]''' are numbers of the form
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<big><big> H = 2<sup>i</sup> × 3<sup>j</sup> × 5<sup>k</sup></big></big>
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where
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<big> i, j, k ≥ 0 </big>
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''Hamming numbers'' are also known as ''ugly numbers'' and also ''5-smooth numbers'' (numbers whose prime divisors are less or equal to 5).
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;Task:
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Generate the sequence of Hamming numbers, ''in increasing order''. In particular:
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# Show the first twenty Hamming numbers.
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# Show the 1691<sup>st</sup> Hamming number (the last one below 2<sup>31</sup>).
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# Show the one million<sup>th</sup> Hamming number (if the language – or a convenient library – supports arbitrary-precision integers).
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;Related tasks:
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* [[Humble numbers]]
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* [[N-smooth numbers]]
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;References:
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* Wikipedia entry: [[wp:Hamming numbers|Hamming numbers]] (this link is re-directed to '''Regular number''').
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* Wikipedia entry: [[wp:Smooth number|Smooth number]]
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* OEIS entry: [[oeis:A051037|A051037 5-smooth or Hamming numbers]]
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* [http://dobbscodetalk.com/index.php?option=com_content&task=view&id=913&Itemid=85 Hamming problem] from Dr. Dobb's CodeTalk (dead link as of Sep 2011; parts of the thread [http://drdobbs.com/blogs/architecture-and-design/228700538 here] and [http://www.jsoftware.com/jwiki/Essays/Hamming%20Number here]).
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<br><br>
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