|
Search: id:A125044
|
|
|
| A125044 |
|
Primes of the form 54k+1 generated recursively. Initial prime is 109. General term is a(n)=Min {p is prime; p divides (R^27 - 1)/(R^9 - 1); Mod[p,27]=1}, where Q is the product of previous terms in the sequence and R = 3Q. |
|
+0
1
|
| |
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
All prime divisors of (R^27 - 1)/(R^9 - 1) different from 3 are congruent to 1 modulo 54.
|
|
REFERENCES
|
M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), p. 209.
|
|
LINKS
|
N. Hobson, Home page (listed in lieu of email address)
|
|
EXAMPLE
|
a(2) = 50221 is the smallest prime divisor congruent to 1 mod
54 of (R^27 - 1)/(R^9 - 1) =
1827509098737085519727094436535854935801097657 = 50221 * 106219 *
342587871163695447795790279515751543, where Q = 109 and R = 3Q.
|
|
CROSSREFS
|
Cf. A000945, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A061724 A145852 A144930 this_sequence A096209 A163597 A087303
Adjacent sequences: A125041 A125042 A125043 this_sequence A125045 A125046 A125047
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
Nick Hobson Nov 18 2006
|
|
|
Search completed in 0.002 seconds
|
