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

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