22 lines
987 B
Text
22 lines
987 B
Text
In number theory, '''Sylvester's sequence''' is an integer sequence in which each term of the sequence is the product of the previous terms, plus one.
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Its values grow doubly exponentially, and the sum of its reciprocals forms a series of unit fractions that converges to '''1''' more rapidly than any other series of unit fractions with the same number of terms.
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Further, the sum of the first '''k''' terms of the infinite series of reciprocals provides the closest possible underestimate of '''1''' by any k-term Egyptian fraction.
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;Task:
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* Write a routine (function, procedure, generator, whatever) to calculate '''Sylvester's sequence'''.
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* Use that routine to show the values of the first '''10''' elements in the sequence.
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* Show the sum of the reciprocals of the first '''10''' elements on the sequence, ideally as an exact fraction.
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;Related tasks:
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* [[Egyptian fractions]]
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* [[Harmonic series]]
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;See also:
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* [[oeis:A000058|OEIS A000058 - Sylvester's sequence]]
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<br>
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