Intended for: July 25, 2012
Timetable
- First draft entered by Alonso del Arte on July 22, 2011 based on comments by Pab Ter and Nestor Romeral Andres. ✓
- Draft reviewed by Daniel Forgues on July 25, 2011 ✓
- Draft to be approved by June 25, 2012
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A000058:
Sylvester’s sequence, which gives the denominators
for the
greedy Egyptian representation of
1.
-
(Of course the numerators are given by A000012.)
The denominators are given by the quadratic recurrence
a (1) | = 2; |
a (n) | = a (n − 1) [a (n − 1) − 1] + 1 |
| = a (n − 1) 2 − a (n − 1) + 1, n ≥ 2.
|
|
and by the formula (which shows that it is an infinite coprime sequence)
-
where for
we get
1 + (empty product, i.e.
1) = 2.