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A124988 Primes of the form 12k+7 generated recursively. Initial prime is 7. General term is a(n)=Min {p is prime; p divides 3+4Q^2; Mod[p,12]=7}, where Q is the product of previous terms in the sequence. 1
7, 199, 7761799, 487, 67, 103, 1482549740515442455520791, 31, 139, 787, 19, 39266047, 1955959, 50650885759, 367, 185767, 62168707 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All prime divisors of 3+4Q^2 are congruent to 1 modulo 6.

At least one prime divisor of 3+4Q^2 is congruent to 3 modulo 4 and hence to 7 modulo 12.

The first six terms are the same as those of A057204.

LINKS

Table of n, a(n) for n=1..17.

N. Hobson, Home page (listed in lieu of email address)

EXAMPLE

a(3) = 1482549740515442455520791 is the smallest prime divisor congruent to 7 mod 12 of 3+4Q^2 = 5281642303363312989311974746340327 = 3562539697 * 1482549740515442455520791, where Q = 7 * 199 * 7761799 * 487 * 67 * 103.

MATHEMATICA

a={7}; q=1;

For[n=2, n<=7, n++,

    q=q*Last[a];

    AppendTo[a, Min[Select[FactorInteger[4*q^2+3][[All, 1]], Mod[#, 12]==7 &]]];

    ];

a (* Robert Price, Jul 15 2015 *)

CROSSREFS

Cf. A000945, A068229, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Sequence in context: A178319 A202943 A057204 * A220934 A221288 A276537

Adjacent sequences:  A124985 A124986 A124987 * A124989 A124990 A124991

KEYWORD

more,nonn

AUTHOR

Nick Hobson, Nov 18 2006

STATUS

approved

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Last modified June 18 10:32 EDT 2021. Contains 345098 sequences. (Running on oeis4.)