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Sylvester's sequence: Difference between revisions
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{{Wikipedia|Sylvester's sequence}}
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.▼
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. 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.▼
▲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.
▲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.
;Task▼
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.
* Write a routine (function, procedure, generator, whatever) to calculate '''Sylvester's sequence'''.▼
* Use that routine to show the values of the first '''10''' elements in the sequence.▼
▲;Task:
▲* Write a routine (function, procedure, generator, whatever) to calculate '''Sylvester's sequence'''.
▲* Use that routine to show the values of the first '''10''' elements in the sequence.
* Show the sum of the reciprocals of the first '''10''' elements on the sequence;
;Related tasks:
;See also: ▼
;* [[oeis:A000058|OEIS A000058 - Sylvester's sequence]]▼
▲;See also:
▲;* [[Egyptian fractions]]
▲;* [[Harmonic series]]
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=={{header|ALGOL 68}}==
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