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A073639
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Numbers n such that x^n + x + 1 is a primitive polynomial modulo 2.
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6
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2, 3, 4, 6, 7, 15, 22, 60, 63, 127, 153, 471, 532, 865, 900, 1366
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Subsequence of A002475 that gives n for which the polynomial x^n + x + 1 is irreducible modulo 2. Term m of A002475 belongs to this sequence iff A046932(m)=2^m-1.
Note that a(16) = 1366 = A002475(23). For n = A002475(24) and A002475(25), polynomial x^n + x + 1 is not primitive modulo 2, so a(17) >= A002475(26) = 4495.
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REFERENCES
| 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.
N. Zierler, On x^n+x+1 over GF(2). Information and Control 16 1970 502-505.
N. Zierler, Primitive trinomials whose degree is a Mersenne exponent. Information and Control 15 1969 67-69.
N. Zierler and J. Brillhart, On primitive trinomials (mod 2). Information and Control 13 1968 541-554.
N. Zierler and J. Brillhart, On primitive trinomials (mod 2), II. Information and Control 14 1969 566-569.
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LINKS
| Joerg Arndt, Fxtbook
R. P. Brent, Searching for primitive trinomials (mod 2)
R. P. Brent, S. Larvala and P. Zimmermann, A fast algorithm for testing reducibility of trinomials ..., Math. Comp. 72 (2003), 1443-1452.
Index entries for sequences related to trinomials over GF(2)
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CROSSREFS
| Cf. A002475, A073571, A057486.
Sequence in context: A039059 A151892 A162570 * A130776 A077292 A171249
Adjacent sequences: A073636 A073637 A073638 * A073640 A073641 A073642
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KEYWORD
| nonn,nice,more
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AUTHOR
| Richard Brent and Paul Zimmermann, Sep 05, 2002.
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