Template:Sequence of the Day for July 6

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 ✓

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A036236: Least inverse of A015910: smallest integer

k > 0

such that

2 k mod k = n, n ≥ 0,

or 0 if no such

k

exists.

{ 1, 0, 3, 4700063497, 6, 19147, 10669, 25, ... }

2 p ≡ 2 (mod p)

for odd prime

p

, and on some random day long ago I got to wondering what values

2 n mod n

might take for other

n

. I did some experimenting and found that that for small

n

,

2 n mod n

took on many small values, but 1 and 3 remained elusive. I asked about them on the seqfan list, and found that

2 n mod n = 1

is provably insoluble, while D. H. Lehmer had found the impressively large minimal solution

n = 4700063497

for

2 n mod n = 3

, an impressively large solution for such a simple identity. Joe K. Crump has done some amazing work with this sequence, see

.