Search: id:A001153
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%I A001153 M0678 N0250
%S A001153 2,3,5,7,17,31,89,127,521,607,1279,2281,3217,4423,9689,19937,
%T A001153 23209,44497,110503,132049,756839,859433,3021377,6972593
%N A001153 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 
               (mod 2) for some k with 0 < k < n.
%C A001153 None exist for the latest Mersenne prime, 13466917, so until a new Mersenne 
               prime is discovered, this sequence is complete. - Paul Zimmermann, 
               Sep 05 2002.
%C A001153 Also the list of "irreducible Mersenne trinomials" since here irreducible 
               implies primitive.
%D A001153 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.
%D A001153 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001153 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001153 N. Zierler, On x^n+x+1 over GF(2). Information and Control 16 1970 502-505.
%D A001153 N. Zierler, Primitive trinomials whose degree is a Mersenne exponent. 
               Information and Control 15 1969 67-69.
%D A001153 N. Zierler and J. Brillhart, On primitive trinomials (mod 2). Information 
               and Control 13 1968 541-554.
%D A001153 N. Zierler and J. Brillhart, On primitive trinomials (mod 2), II. Information 
               and Control 14 1969 566-569.
%H A001153 R. P. Brent, <a href="http://wwwmaths.anu.edu.au/~brent/trinom-old.html">
               Searching for primitive trinomials (mod 2)</a>
%H A001153 R. P. Brent, <a href="ftp://ftp.comlab.ox.ac.uk/pub/Documents/techpapers/
               Richard.Brent/trinom/table.txt">Tables of trinomials</a>
%H A001153 R. P. Brent, S. Larvala and P. Zimmermann, <a href="http://wwwmaths.anu.edu.au/
               ~brent/pd/rpb199.pdf">A fast algorithm for testing reducibility of 
               trinomials ...</a>, Math. Comp. 72 (2003), 1443-1452.
%H A001153 A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, <a href="http:/
               /www.cacr.math.uwaterloo.ca/hac/">Handbook of Applied Cryptography</
               a>, CRC Press, 1996; see p. 162.
%H A001153 <a href="Sindx_Tri.html#trinomial">Index entries for sequences related 
               to trinomials over GF(2)</a>
%Y A001153 Cf. A002475, A000043, A073571, A073639, A057486, A073726.
%Y A001153 For values of k see A074743.
%Y A001153 Sequence in context: A103383 A103382 A143027 this_sequence A141453 A100532 
               A040149
%Y A001153 Adjacent sequences: A001150 A001151 A001152 this_sequence A001154 A001155 
               A001156
%K A001153 nonn,nice
%O A001153 1,1
%A A001153 N. J. A. Sloane (njas(AT)research.att.com).
%E A001153 Corrected and extended by Paul Zimmermann, Sep 05, 2002.

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