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A124984 Primes of the form 8k+3 generated recursively. Initial prime is 3. General term is a(n)=Min {p is prime; p divides 2+Q^2; Mod[p,8]=3}, where Q is the product of previous terms in the sequence. 19
3, 11, 1091, 1296216011, 2177870960662059587828905091, 76870667, 19, 257680660619, 73677606898727076965233531, 23842300525435506904690028531941969449780447746432390747, 35164737203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

2+Q^2 always has a prime divisor congruent to 3 modulo 8.

REFERENCES

D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 191.

LINKS

Robert Price, Table of n, a(n) for n = 1..15

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

EXAMPLE

a(3) = 1091 is the smallest prime divisor congruent to 3 mod 8 of 2+Q^2 = 1091, where Q = 3 * 11.

MATHEMATICA

a = {3}; q = 1;

For[n = 2, n ≤ 5, n++,

    q = q*Last[a];

    AppendTo[a, Min[Select[FactorInteger[2 + q^2][[All, 1]], Mod[#,

    8] \[Equal] 3 &]]];

    ];

a (* Robert Price, Jul 14 2015 *)

CROSSREFS

Cf. A000945, A007520, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Sequence in context: A264725 A088579 A006938 * A287432 A034797 A212814

Adjacent sequences:  A124981 A124982 A124983 * A124985 A124986 A124987

KEYWORD

more,nonn

AUTHOR

Nick Hobson, Nov 18 2006

EXTENSIONS

a(10) from Robert Price, Jul 04 2015

a(11) from Robert Price, Jul 05 2015

STATUS

approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)