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 A057460 Numbers n such that x^n + x^2 + 1 is irreducible over GF(2). 3
 1, 3, 5, 11, 21, 29, 35, 93, 123, 333, 845, 4125, 10437, 10469, 14211, 20307, 34115, 47283, 50621, 57341 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Joerg Arndt, Matters Computational (The Fxtbook) I. F. Blake, S. Gao and R. J. Lambert, Constructive problems for irreducible polynomials over finite fields, in Information Theory and Applications, LNCS 793, Springer-Verlag, Berlin, 1994, 1-23, See Table 2. H. Fredricksen, R. Wisniewski, On trinomials x^n + x^2 + 1 and x^{8l+-1} + x^k + 1 irreducible overGF(2), Inform. and Control 50 (1981), no. 1, 58--63. MR0665139 (84i:12013). Gives first 20 terms. MATHEMATICA Do[ If[ ToString[ Factor[ x^n + x^2 + 1, Modulus -> 2 ] ] == ToString[ x^n + x^2 + 1 ], Print[ n ] ], {n, 0, 750} ] PROG (PARI) isok(n) = polisirreducible(Mod(1, 2)*(x^n + x^2 + 1)); \\ Michel Marcus, Aug 23 2015 CROSSREFS Cf. A002475, A074710. Sequence in context: A281318 A082713 A074710 * A269112 A093328 A045515 Adjacent sequences:  A057457 A057458 A057459 * A057461 A057462 A057463 KEYWORD nonn,more AUTHOR Robert G. Wilson v, Sep 27 2000 EXTENSIONS Confirmed by Richard P. Brent, Sep 05 2002 STATUS approved

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Last modified February 24 16:26 EST 2020. Contains 332209 sequences. (Running on oeis4.)