OFFSET
2,4
COMMENTS
This is the format used by John Brillhart (1968) and Zierler and Brillhart (1968).
REFERENCES
Alanen, J. D., and Donald E. Knuth. "Tables of finite fields." Sankhyā: The Indian Journal of Statistics, Series A (1964): 305-328.
John Brillhart, On primitive trinomials (mod 2), unpublished Bell Labs Memorandum, 1968.
Marsh, Richard W. Table of irreducible polynomials over GF (2) through degree 19. Office of Technical Services, US Department of Commerce, 1957.
LINKS
Robert Israel, Table of n, a(n) for n = 2..4328 (rows 2 to 2170, flattened)
Joerg Arndt, Complete list of primitive trinomials over GF(2) up to degree 400. (Lists primitive trinomials only.)
Joerg Arndt, Complete list of primitive trinomials over GF(2) up to degree 400 [Cached copy, with permission]
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 Table 4.6.
Svein Mossige, Table of irreducible polynomials over GF[2] of degrees 10 through 20, Mathematics of Computation 26.120 (1972): 1007-1009.
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.
EXAMPLE
Triangle begins:
1,
1,
1,
2,
1, 3,
1, 3,
-1,
1, 4,
3,
2,
3, 5,
-1,
5,
1, 4, 7,
-1,
3, 5, 6,
...
MAPLE
T:= proc(n) local L; L:= select(k -> Irreduc(x^n+x^k+1) mod 2, [$1..n/2]); if L = [] then -1 else op(L) fi
end proc:
map(T, [$2..100]); # Robert Israel, Mar 28 2017
MATHEMATICA
DeleteCases[#, 0] & /@ Table[Boole[IrreduciblePolynomialQ[x^n + x^# + 1, Modulus -> 2]] # & /@ Range[Floor[n/2]], {n, 2, 40}] /. {} -> {-1} // Flatten (* Michael De Vlieger, Mar 28 2017 *)
CROSSREFS
KEYWORD
sign,tabf,more
AUTHOR
N. J. A. Sloane, Nov 27 2016
STATUS
approved