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A001153
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Degrees of primitive irreducible trinomials: n such that 2^n - 1 is a Mersenne prime and x^n + x^k + 1 is a primitive irreducible polynomial over GF(2) for some k with 0 < k < n.
(Formerly M0678 N0250)
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5
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2, 3, 5, 7, 17, 31, 89, 127, 521, 607, 1279, 2281, 3217, 4423, 9689, 19937, 23209, 44497, 110503, 132049, 756839, 859433, 3021377, 6972593, 24036583, 25964951, 30402457, 32582657, 42643801, 43112609
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OFFSET
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1,1
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COMMENTS
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Also the list of "irreducible Mersenne trinomials" since here irreducible implies primitive.
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REFERENCES
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Kurita, Yoshiharu and Matsumoto, Makoto; Primitive t-nomials (t=3,5) over GF(2) whose degree is a Mersenne exponent <= 44497. Math. Comp. 56 (1991), no. 194, 817-821.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
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Table of n, a(n) for n=1..30.
R. P. Brent, Searching for primitive trinomials (mod 2)
R. P. Brent, Trinomial Log Files and Certificates
R. P. Brent, Tables of trinomials (outdated)
R. P. Brent, S. Larvala and P. Zimmermann, A fast algorithm for testing reducibility of trinomials ..., Math. Comp. 72 (2003), 1443-1452.
A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996; see p. 162.
Index entries for sequences related to trinomials over GF(2)
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CROSSREFS
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Cf. A002475, A000043, A073571, A073639, A057486, A073726.
For smallest values of k, see A074743.
Sequence in context: A103383 A103382 A143027 * A141453 A100532 A040149
Adjacent sequences: A001150 A001151 A001152 * A001154 A001155 A001156
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Corrected and extended by Paul Zimmermann, Sep 05, 2002.
Six more terms from Brent's page added by Max Alekseyev, Oct 22 2011
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STATUS
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approved
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