A074743 Smallest k such that trinomial x^A001153(n) + x^k + 1 over GF(2) is primitive.

1, 1, 2, 1, 3, 3, 38, 1, 32, 105, 216, 715, 67, 271, 84, 881, 1530, 8575, 25230, 7000, 215747, 170340, 361604, 3037958, 8412642, 880890, 2162059, 5110722, 55981, 3569337

Offset: 1

Author

N. J. A. Sloane, Sep 06 2002

Keywords

• nonn
• more

Links

• R. P. Brent, Trinomial Log Files and Certificates
• 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)

Programs

Maple

for n from 1 to 16 do for k from 1 to A001153(n)-1 do if(Primitive(x^A001153(n) + x^k + 1) mod 2)then printf("%d, ",k): break: fi:od:od: # Nathaniel Johnston, Apr 21 2011

Extensions

a(8)-a(16) from Nathaniel Johnston, Apr 21 2011

a(17)-a(30) from Brent's data added by Max Alekseyev, Oct 22 2011