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Search: id:A117223
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| A117223 |
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Numbers n such that Phi(n,x) is a flat cyclotomic polynomial of order three. |
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+0
5
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| 231, 399, 435, 465, 483, 651, 663, 741, 861, 885, 903, 915, 1113, 1173, 1209, 1281, 1311, 1335, 1353, 1443, 1479, 1533, 1581, 1599, 1653, 1743, 1833, 1947, 2163, 2211, 2235, 2247, 2265, 2301, 2337, 2379, 2409, 2485, 2667, 2685, 2715, 2829, 2877, 2915
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A flat polynomial is defined to be a polynomial whose coefficients are -1, 0, or 1. Order three means that n is the product of three odd primes p<q<r. Bachman shows that for each p there are an infinite number of pairs {q,r} that generate flat cyclotomic polynomials. It is well known that all cyclotomic polynomials of orders one and two are flat. There are no flat cyclotomic polynomials of order four for n<10^5.
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REFERENCES
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Gennady Bachman, Flat cyclotomic polynomials of order three, Bull. London Math. Soc. 38 (2006), 53-60.
Nathan Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), 118-126.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
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IsOrder3[n_] := (n>1) && OddQ[n] && Transpose[FactorInteger[n]][[2]] == {1, 1, 1}; PolyHeight[p_] := Max[Abs[CoefficientList[p, x]]]; Clear[x]; Select[Range[4000], IsOrder3[ # ] && PolyHeight[Cyclotomic[ #, x]]==1&]
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CROSSREFS
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Cf. A117318 (fourth-order flat cyclotomic polynomials).
Sequence in context: A031965 A088289 A046009 this_sequence A029569 A066370 A139412
Adjacent sequences: A117220 A117221 A117222 this_sequence A117224 A117225 A117226
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Mar 04 2006
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