|
Search: id:A124993
|
|
|
| A124993 |
|
Primes of the form 22k+1 generated recursively. Initial prime is 23. General term is a(n)=Min {p is prime; p divides (R^11 - 1)/(R - 1); Mod[p,11]=1}, where Q is the product of previous terms in the sequence, and R = 11Q. |
|
+0
18
|
|
| 23, 4847239, 2971, 3936923, 9461, 1453, 331, 81373909, 89
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
All prime divisors of (R^11 - 1)/(R - 1) different from 11 are congruent to 1 modulo 22.
|
|
REFERENCES
|
M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), pp. 208-209.
|
|
LINKS
|
N. Hobson, Home page (listed in lieu of email address)
|
|
EXAMPLE
|
a(3) = 2971 is the smallest prime divisor congruent to 1 mod 22
of (R^11 - 1)/(R - 1) =
7693953366218628230903493622259922359469805176129784863956847906415055607909988155588181877
= 2971 * 357405886421 * 914268562437006833738317047149 *
7925221522553970071463867283158786415606996703, where Q = 23 * 4847239,
and R = 11Q.
|
|
CROSSREFS
|
Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A013772 A034247 A050234 this_sequence A013818 A087527 A013906
Adjacent sequences: A124990 A124991 A124992 this_sequence A124994 A124995 A124996
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
Nick Hobson Nov 18 2006
|
|
|
Search completed in 0.002 seconds
|
