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# User:Daniel Forgues

Daniel Forgues

kephalopod

B.Sc. (Physics)

Université de Montréal (1982)

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## OEIS Wiki

### My subpages

 User:Daniel Forgues/Contributions Partial commented lists of my previous, in progress and future contributions. User:Daniel Forgues/Copy and paste Tables and other stuff ready for copying and pasting.

 Coord. Universal Time

 Tuesday, July 25, 2017

14:42

 OEIS Wiki Server Time

 Tuesday, July 25, 2017

10:42

## Sequence of the Day for July 25

A000058: Sylvester's sequence, which gives the denominators
 a (n)
for the greedy Egyptian representation of
 1
.
$1 = \frac{1}{2} + \frac{1}{3} + \frac{1}{7} + \frac{1}{43} + \frac{1}{1807} + \ldots \,$

(Of course the numerators are given by A000012.)

The denominators are given by the quadratic recurrence

\begin{array}{l} {\displaystyle \begin{align} a(1) &= 2; \\ a(n) &= a(n-1) (a(n-1) - 1) + 1 \\ &= a(n)^2 - a(n) + 1,\quad n \ge 2. \end{align} } \end{array}

and by the formula (which shows that it is an infinite coprime sequence)

$a(n) = 1 + \prod_{i=1}^{n-1} a(i), \,$
where for
 n = 1
we get
 1 + (
empty product, i.e.
 1) = 2
.

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