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Template:Sequence of the Day for July 8

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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
Yesterday's SOTD * Tomorrow's SOTD

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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
are called Carmichael numbers.