Sylvester's Sequence - Formal Definitions

Formal Definitions

Formally, Sylvester's sequence can be defined by the formula

The product of an empty set is 1, so s0 = 2.

Alternatively, one may define the sequence by the recurrence

with s0 = 2.

It is straightforward to show by induction that this is equivalent to the other definition.

Read more about this topic:  Sylvester's Sequence

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