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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 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 5 23:10 EDT 2020. Contains 334858 sequences. (Running on oeis4.)