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 A057207 a(1)=5, a(n) is the smallest prime dividing 4*Q^2 + 1 where Q is the product of all previous terms in the sequence. 4
 5, 101, 1020101, 53, 29, 2507707213238852620996901, 449, 13, 8693, 1997, 6029, 61, 3181837, 113, 181, 1934689, 6143090225314378441493352126119201470973493456817556328833988172277, 4733, 3617, 41, 68141, 37, 51473, 17, 821, 598201519454797, 157, 9689, 2357, 757, 149, 293, 5261 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Removed redundant mod(p,4) = 1 criterion from definition.  By quadratic reciprocity, all factors of 1 + 4Q^2 are congruent to 1 (mod 4). See comments at the end of the b-file for an additional eight terms not proved, but nevertheless highly likely to be correct. - Daran Gill, Mar 23 2013 REFERENCES P. G. L. Dirichlet (1871): Vorlesungen über 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 Daran Gill, Table of n, a(n) for n = 1..33 Mersenne Forum, Sequence A057207 OEIS wiki, OEIS sequences needing factors EXAMPLE a(4)=53 is the smallest prime divisor of 4*(5.101.1020101)^2+1 = 1061522231810040101 = 53*1613*12417062216309. MATHEMATICA t = {5}; Do[q = Times @@ t; AppendTo[t, FactorInteger[1 + 4*q^2][[1, 1]]], {6}]; t (* T. D. Noe, Mar 27 2013 *) CROSSREFS Cf. A000945, A000946, A005265, A005266, A051308-A051335, A002144, A057204-A057208. Sequence in context: A009765 A113073 A275749 * A124986 A231830 A260024 Adjacent sequences:  A057204 A057205 A057206 * A057208 A057209 A057210 KEYWORD nonn AUTHOR Labos Elemer, Oct 09 2000 EXTENSIONS Eight more terms, a(9)-a(16), from Max Alekseyev, Apr 27 2009 Seventeen more terms, a(17)-a(33), added by Daran Gill, Mar 23 2013 STATUS approved

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Last modified June 4 03:40 EDT 2020. Contains 334815 sequences. (Running on oeis4.)