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A057461 Numbers n such that x^n + x^3 + 1 is irreducible over GF(2). 2
1, 2, 4, 5, 6, 7, 10, 12, 17, 18, 20, 25, 28, 31, 41, 52, 66, 130, 151, 180, 196, 503, 650, 761, 986, 1391, 1596, 2047, 2700, 4098, 6172, 6431, 6730, 8425, 10162, 11410, 12071, 13151, 14636, 17377, 18023, 30594, 32770, 65538, 77047, 81858 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Next term is > 10^5. [Joerg Arndt, Apr 28 2012]

LINKS

Table of n, a(n) for n=1..46.

Joerg Arndt, Matters Computational (The Fxtbook), section 40.9.3 "Irreducible trinomials of the form 1 + x^k + x^d", p.850

MATHEMATICA

Do[ If[ ToString[ Factor[ x^n + x^3 + 1, Modulus -> 2 ] ] == ToString[ x^n + x^3 + 1 ], Print[ n ] ], {n, 0, 750} ]

PROG

(PARI)

for (n=1, 5000, if ( polisirreducible(Mod(1, 2)*(x^n+x^3+1)), print1(n, ", ") ) );

/* Joerg Arndt, Apr 28 2012 */

(Sage)

P.<x> = GF(2)[]

for n in range(10^4):

    if (x^n+x^3+1).is_irreducible():

        print(n) # Joerg Arndt, Apr 28 2012

CROSSREFS

Cf. A002475.

Sequence in context: A129132 A191843 A318606 * A070116 A246965 A300861

Adjacent sequences:  A057458 A057459 A057460 * A057462 A057463 A057464

KEYWORD

nonn,hard

AUTHOR

Robert G. Wilson v, Sep 27 2000

EXTENSIONS

a(24) - a(29) from Robert G. Wilson v, Aug 06 2010

Terms >= 4098 by Joerg Arndt, Apr 28 2012.

STATUS

approved

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Last modified February 26 01:41 EST 2020. Contains 332270 sequences. (Running on oeis4.)