Template:Sequence of the Day for July 8

Intended for: July 8, 2012

Timetable

First draft entered by Alonso del Arte on March 12, 2011 based on an almost verbatim copy of a write-up by Karsten Meyer from January 1, 2011. ✓
Draft reviewed by Daniel Forgues on May 5, 2011 ✓
Draft approved by Alonso del Arte on July 7, 2011 ✓

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A181780: Numbers

n

which are Fermat pseudoprimes to some base

b

, with

2 ≤ b ≤ n − 2

.

{ 15, 21, 25, 28, 33, 35, 39, ... }

For example 15 is Fermat pseudoprime to every base of the form

15k + 4

and

15k + 11

with

k ≥ 0

. The sequence shows that the distribution of the Fermat pseudoprimes is the opposite of rare, if it is not determined on a fixed base

b

. There are 429 Fermat pseudoprimes below 1000, but only 168 prime numbers. Fermat pseudoprimes to all bases

b

, with

2 ≤ b ≤ n − 2