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Search: id:A073726
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| A073726 |
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Primitive irreducible trinomials: x^n + x^k + 1 is a primitive irreducible polynomial (mod 2) for some k with 0 < k < n. |
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+0
6
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| 2, 3, 4, 5, 6, 7, 9, 10, 11, 15, 17, 18, 20, 21, 22, 23, 25, 28, 29, 31, 33, 35, 36, 39, 41, 47, 49, 52, 55, 57, 58, 60, 63, 65, 68, 71, 73, 79, 81, 84, 87, 89, 93, 94, 95, 97, 98, 100
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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S. W. Golomb, "Shift Register Sequence", revised edition, reprinted by Aegean Park Press, 1982. See Tables V-1, V-2.
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LINKS
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Joerg Arndt, Fxtbook
A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996; see Table 4.8.
Index entries for sequences related to trinomials over GF(2)
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PROGRAM
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(MAGMA) A073726 := function(n) for k := 1 to n-1 do if IsPrimitive(x^n+x^k+1) then return true; end if; end for; return false; end function; l := []; for n := 1 to 100 do if A073726(n) then l := Append(l, n); end if; end for; l;
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CROSSREFS
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See A073726 for irreducible trinomials and A001153 for primitive Mersenne trinomials (and references). See A074744 for values of k.
Sequence in context: A123101 A071557 A117729 this_sequence A008839 A039226 A039271
Adjacent sequences: A073723 A073724 A073725 this_sequence A073727 A073728 A073729
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KEYWORD
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nonn,nice
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AUTHOR
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Richard Brent and Paul Zimmermann, Sep 05 2002
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