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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
13, 28393, 128758492789, 73, 193, 37, 457, 8363172060732903211423577787181 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 5 20:57 EST 2023. Contains 360087 sequences. (Running on oeis4.)