|
| |
|
|
A002475
|
|
Numbers n such that x^n + x + 1 is irreducible over GF(2).
(Formerly M0544 N0194)
|
|
16
| |
|
|
0, 2, 3, 4, 6, 7, 9, 15, 22, 28, 30, 46, 60, 63, 127, 153, 172, 303, 471, 532, 865, 900, 1366, 2380, 3310, 4495, 6321, 7447, 10198, 11425, 21846, 24369, 27286, 28713, 32767, 34353, 46383, 53484, 62481, 83406, 87382
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| n=1 is excluded since the polynomial "1" is not normally regarded as irreducible.
|
|
|
REFERENCES
| 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).
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 975.
N. Zierler, On x^n+x+1 over GF(2). Information and Control 16 1970 502-505.
|
|
|
LINKS
| Joerg Arndt, Fxtbook
Index entries for sequences related to trinomials over GF(2)
|
|
|
MATHEMATICA
| Do[ If[ ToString[ Factor[ x^n + x + 1, Modulus -> 2 ] ] == ToString[ x^n + x + 1 ], Print [ n ] ], {n, 0, 28713} ]
|
|
|
PROG
| (MAGMA) P<x> := PolynomialRing(GaloisField(2)); for n := 2 to 100000 do if IsIrreducible(x^n+x+1) then print(n); end if; endfor;
(Sage)
P.<x> = GF(2)[]
for n in range(100000):
if (x^n+x+1).is_irreducible():
print(n) # Ruperto Corso, Dec 11 2011
|
|
|
CROSSREFS
| Cf. A001153, A073639.
Sequence in context: A055494 A165773 A064414 * A057519 A155905 A047518
Adjacent sequences: A002472 A002473 A002474 * A002476 A002477 A002478
|
|
|
KEYWORD
| nonn,more,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Two more terms from Paul Zimmermann, Sep 05, 2002
a(37)-a(39) from Max Alekseyev (maxale(AT)gmail.com), Oct 29 2011
Two more terms from Ruperto Corso (rupertocorsoto(AT)gmail.com), Dec 11 2011
|
| |
|
|
