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Search: id:A134547
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| 29, 64, 109, 164, 229, 304, 389, 484, 589, 704, 829, 964, 1109, 1264, 1429, 1604, 1789, 1984, 2189, 2404, 2629, 2864, 3109, 3364, 3629, 3904, 4189, 4484, 4789, 5104
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OFFSET
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1,1
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COMMENT
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Most quintic polynomials x^5 + 5x(5*n^2+20n+4) + 8(5*n^2+20n+4) (with the exception of n=0 or 4 when the polynomial is solvable, or n=-2 when it is reducible) have nonsolvable alternating Galois group A5 (of order 60) over rational numbers.
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FORMULA
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G.f.: -x*(29-23*x+4*x^2)/(-1+x)^3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
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MATHEMATICA
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Table[5n^2 + 20n + 4, {n, 1, 30}]
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CROSSREFS
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Cf. A134538.
Sequence in context: A046275 A092222 A039516 this_sequence A044131 A044512 A118481
Adjacent sequences: A134544 A134545 A134546 this_sequence A134548 A134549 A134550
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Oct 31 2007, Nov 21 2007
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