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Search: id:A002475
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| A002475 |
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Numbers n such that x^n + x + 1 is irreducible over GF(2).
(Formerly M0544 N0194)
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+0
17
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| 0, 2, 3, 4, 6, 7, 9, 15, 22, 28, 30, 46, 60, 63, 127, 153, 172, 303, 471, 532, 865, 900, 1366, 2380, 3310, 4495, 6321, 7447, 10198, 11425, 21846, 24369, 27286, 28713, 32767, 34353
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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n=1 is excluded since the polynomial "1" is not normally regarded as irreducible.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 975.
N. Zierler, On x^n+x+1 over GF(2). Information and Control 16 1970 502-505.
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LINKS
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Joerg Arndt, Fxtbook
Index entries for sequences related to trinomials over GF(2)
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MATHEMATICA
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Do[ If[ ToString[ Factor[ x^n + x + 1, Modulus -> 2 ] ] == ToString[ x^n + x + 1 ], Print [ n ] ], {n, 0, 28713} ]
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PROGRAM
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(MAGMA) P<x> := PolynomialRing(GaloisField(2)); for n := 2 to 100000 do if IsIrreducible(x^n+x+1) then print(n); end if; endfor;
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CROSSREFS
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Cf. A001153, A073639.
Adjacent sequences: A002472 A002473 A002474 this_sequence A002476 A002477 A002478
Sequence in context: A055494 A165773 A064414 this_sequence A057519 A155905 A047518
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Two more terms from Paul Zimmermann, Sep 05, 2002
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