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 A217759 Primes of the form 4k+3 generated recursively: a(1)=3, a(n)= Min{p; p is prime; Mod[p,4]=3; p|4Q^2-1}, where Q is the product of all previous terms in the sequence. 2
 3, 7, 43, 19, 6863, 883, 23, 191, 2927, 205677423255820459, 11, 163, 227, 9127, 59, 31, 71, 131627, 2101324929412613521964366263134760336303, 127, 1302443, 4065403, 107, 2591, 21487, 223, 12823, 167, 53720906651, 5452254637117019, 39827899, 11719, 131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Contrast A057207, where all the factors are congruent to 1 (mod 4), here only one is guaranteed to be congruent to 3 (mod 4). 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, p. 13. LINKS Daran Gill, Table of n, a(n) for n = 1..51 Mersenne Forum, Two new sequences EXAMPLE a(10) is 205677423255820459 because it is the only prime factor congruent to 3 (mod 4) of 4*(3*7*43*19*6863*883*23*191*2927)^2-1 = 5*13*2088217*256085119729*205677423255820459. The four smaller factors are all congruent to 1 (mod 4). CROSSREFS Cf. A000945, A000946, A005265, A005266, A051308-A051335, A002145, A057204-A057208. Sequence in context: A229941 A019018 A018993 * A160615 A106965 A257366 Adjacent sequences:  A217756 A217757 A217758 * A217760 A217761 A217762 KEYWORD nonn AUTHOR Daran Gill, Mar 23 2013 STATUS approved

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Last modified January 22 16:29 EST 2020. Contains 331152 sequences. (Running on oeis4.)