Template:Sequence of the Day for July 23

Intended for: July 23, 2012

Timetable

• First draft entered by Alonso del Arte on July 22, 2011 ✓
• Draft reviewed by Daniel Forgues on July 23, 2011 ✓
• Draft to be approved by June 23, 2012

Yesterday's SOTD * Tomorrow's SOTD

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A000945: The Euclid–Mullin sequence:

a (1) = 2

; for

n   ≥   2

,

a (n)

is the smallest prime factor of

1 + ∏ n  − 1 k  = 1  a (k)

.

{ 2, 3, 7, 43, 13, 53, 5, 6221671, ... }

The first four terms coincide with the Sylvester sequence (where each term is the product of all preceding terms plus 1) (A000058), a [thus strictly increasing] infinite coprime sequence whose terms may be prime or composite.