|
| |
|
|
A124990
|
|
Primes of the form 12k+1 generated recursively. Initial prime is 13. General term is a(n)=Min {p is prime; p divides Q^4-Q^2+1}, where Q is the product of previous terms in the sequence.
|
|
2
|
| |
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
All prime divisors of Q^4 - Q^2 + 1 are congruent to 1 modulo 12.
|
|
|
REFERENCES
|
K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, NY, Second Edition (1990), p. 63.
|
|
|
LINKS
|
Table of n, a(n) for n=1..8.
N. Hobson, Home page (listed in lieu of email address)
|
|
|
EXAMPLE
|
a(3) = 128758492789 is the smallest prime divisor of Q^4 - Q^2 + 1 = 18561733755472408508281 = 128758492789 * 144159296629, where Q = 13 * 28393.
|
|
|
MATHEMATICA
|
a = {13}; q = 1;
For[n = 2, n ≤ 8, n++,
q = q*Last[a];
AppendTo[a, Min[Select[FactorInteger[q^4 - q^2 + 1][[All, 1]],
Mod[#, 12] == 1 &]]];
];
a (* Robert Price, Jun 25 2015 *)
|
|
|
CROSSREFS
|
Cf. A000945, A068228, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.
Sequence in context: A185408 A123921 A145716 * A013752 A076811 A203691
Adjacent sequences: A124987 A124988 A124989 * A124991 A124992 A124993
|
|
|
KEYWORD
|
more,nonn
|
|
|
AUTHOR
|
Nick Hobson, Nov 18 2006
|
|
|
EXTENSIONS
|
a(8) from Robert Price, Jun 25 2015
|
|
|
STATUS
|
approved
|
| |
|
|
