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Search: id:A020501
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| A020501 |
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Cyclotomic polynomials at x=-2. |
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+0
4
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| -2, -3, -1, 3, 5, 11, 7, 43, 17, 57, 31, 683, 13, 2731, 127, 331, 257, 43691, 73, 174763, 205, 5419, 2047, 2796203, 241, 1016801, 8191, 261633, 3277, 178956971, 151, 715827883, 65537, 1397419, 131071, 24214051
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(0) depends on the definition of the 0-th cyclotomic polynomial; Maple defines it as x, but Mathematica defines it as 1. - T. D. Noe, Jul 23 2008 [a(0) = x is correct. - N. J. A. Sloane (njas(AT)research.att.com), Aug 01 2008]
A020501[2n] = A019320[n] for all odd n > 1. (Because if m > 1 is odd, then Phi_2m(x) = Phi_m(-x) as demonstrated by Bloom). - Antti Karttunen Aug 02 2001
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REFERENCES
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Bloom, D.M. "On the Coefficients of the Cyclotomic Polynomials." Amer.Math.Monthly 75, 372-377, 1968.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for cyclotomic polynomials, values at X
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MAPLE
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with(numtheory, cyclotomic); f := n->subs(x=-2, cyclotomic(n, x)); seq(f(i), i=0..64);
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CROSSREFS
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Cf. A020500, A020513.
Cf. A105603
Sequence in context: A054250 A067337 A047973 this_sequence A086404 A152976 A153861
Adjacent sequences: A020498 A020499 A020500 this_sequence A020502 A020503 A020504
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KEYWORD
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sign
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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