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Search: id:A057208
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| A057208 |
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Primes of form 8k+5 generated recursively: a(1)=5 a(n)= Min{p, prime; Mod[p,8]=5; p|4+Q^2}, where Q is the product of all previous terms in the sequence. |
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24
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| 5, 29, 1237, 32171803229, 829, 405565189, 14717, 39405395843265000967254638989319923697097319108505264560061
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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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.
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EXAMPLE
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a(3)=1237=8*154+5 is the smallest suitable prime divisor of (5.29)*5.29+4=21029=17*1237. Albeit 17 is the smallest prime divisor, but 17 is not congruent to 5 modulo 8, so 1237 is the good choice.
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CROSSREFS
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Cf. A000945, A000946, A005265, A005266, A051308-A051335, A007521, A057204-A057208.
Sequence in context: A072880 A112959 A085553 this_sequence A046842 A057706 A057705
Adjacent sequences: A057205 A057206 A057207 this_sequence A057209 A057210 A057211
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KEYWORD
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more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 09 2000
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