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Template:Sequence of the Day for July 6

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Intended for: July 6, 2012

Timetable

  • First draft entered by Alonso del Arte on March 7, 2011 based on an almost verbatim copy of a write-up by David W. Wilson from October 23, 2010. ✓
  • Draft reviewed by Alonso del Arte on March 24, 2012
  • Draft approved by Daniel Forgues on June 6, 2015
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A036236: Least inverse of A015910: smallest integer
k   >   0
such that
2k mod k = n, n   ≥   0,
or 0 if no such
k
exists.
{ 1, 0, 3, 4700063497, 6, 19147, 10669, 25, ... }
Fermat’s little theorem says that
2p   ≡   2  (mod p)
for odd prime
p
, and on some random day long ago I got to wondering what values
2n mod n
might take for other
n
. I did some experimenting and found that that for small
n
,
2n mod n
took on many small values, but 1 and 3 remained elusive. I asked about them on the seqfan list, and found that
2n mod n = 1
is provably insoluble, while D. H. Lehmer had found the impressively large minimal solution
n = 4700063497
for
2n mod n = 3
, an impressively large solution for such a simple identity. Joe K. Crump has done some amazing work with this sequence, see
2n mod n = c
.