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A057205 Primes congruent to 3 modulo 4 generated recursively: a(n) = Min{p, prime; Mod[p,4]=3; p|4Q-1}, where Q is the product of all previous terms in the sequence. The initial term is 3. 1
3, 11, 131, 17291, 298995971, 8779, 594359, 59, 151, 983, 19, 38851089348584904271503421339, 2359886893253830912337243172544609142020402559023, 823818731, 2287, 7, 9680188101680097499940803368598534875039120224550520256994576755856639426217960921548886589841784188388581120523, 163, 83, 1471, 34211, 2350509754734287, 23567 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Dirichlet, P. G. L. (1871): Vorlesungen uber Zahlentheorie. Braunschweig, Viewig, Supplement VI, 24 pages.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, page 13.

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

a(4)=17291=4.4322+3 is the smallest prime divisor congruent to 3 mod 4 of Q=3.11.131-1=17291.

MATHEMATICA

a={3}; q=1;

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

    q=q*Last[a];

    AppendTo[a, Min[Select[FactorInteger[4*q-1][[All, 1]], Mod[#, 4]==3&]]];

    ];

a (* Robert Price, Jul 18 2015 *)

CROSSREFS

Cf. A000945, A000946, A005265, A005266, A051308-A051335, A002476, A057204-A057208.

Sequence in context: A284604 A072878 A112957 * A121897 A067657 A063502

Adjacent sequences:  A057202 A057203 A057204 * A057206 A057207 A057208

KEYWORD

nonn

AUTHOR

Labos Elemer, Oct 09 2000

EXTENSIONS

More terms from Phil Carmody, Sep 18 2005

Terms corrected and extended by Sean A. Irvine, Oct 23 2014

STATUS

approved

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Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)