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Search: id:A057205
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| A057205 |
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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. |
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+0
2
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| 3, 11, 131, 17291, 298995971, 8779, 594359, 59, 151, 983, 19, 38851089348584904271503421339, 52911825449152891889263884724705607883122819555892162265139253510369235550041252\ 39189441555427031534736693540029592818205038297401875090181563033413103
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a[21] requires the factoring of a 303-digit integer. No serious attack on this has been made, as far as I am aware. - Phil Carmody (pc+oeis(AT)asdf.org), Sep 18 2005
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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(4)=17291=4.4322+3 is the smallest prime divisor congruent to 3 mod 4 of Q=3.11.131-1=17291.
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CROSSREFS
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Cf. A000945, A000946, A005265, A005266, A051308-A051335, A002476, A057204-A057208.
Sequence in context: A088076 A072878 A112957 this_sequence A121897 A067657 A063502
Adjacent sequences: A057202 A057203 A057204 this_sequence A057206 A057207 A057208
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 09 2000
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EXTENSIONS
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More terms from Phil Carmody (pc+oeis(AT)asdf.org), Sep 18 2005
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