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A057463 Numbers n such that x^n + x^4 + 1 is irreducible over GF(2). 2
1, 3, 7, 9, 15, 39, 57, 81, 105, 1239, 5569, 9457, 11095, 11631, 12327, 37633, 63247 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(18) is greater than 10^5. - Joerg Arndt, Apr 28 2012

All terms are congruent to 1 or 3 (mod 6). - Robert Israel, Sep 05 2016

LINKS

Table of n, a(n) for n=1..17.

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

EXAMPLE

6 is not in the sequence since x^6 + x^4 + 1 = (x^3 + x^2 + 1)^2, but 7 is in the sequence since x^7 + x^4 + 1 is irreducible. (Trial division by x + 1, x^2 + x + 1, x^3 + x^2 + 1, and x^3 + x + 1) - Michael B. Porter, Sep 06 2016

MAPLE

for m from 1 to 200 do if(Irreduc(x^m + x^4 + 1) mod 2) then printf("%d, ", m):fi:od: # Nathaniel Johnston, Apr 19 2011

MATHEMATICA

Do[ If[ ToString[ Factor[ x^n + x^4 + 1, Modulus -> 2 ] ] == ToString[ x^n + x^4 + 1 ], Print[ n ] ], {n, 0, 750} ]

PROG

(Sage)

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

for n in range(10^4):

    if (x^n+x^4+1).is_irreducible():

        print(n) # Joerg Arndt, Apr 28 2012

CROSSREFS

Cf. A002475.

Sequence in context: A304850 A306740 A320022 * A287124 A118258 A117583

Adjacent sequences:  A057460 A057461 A057462 * A057464 A057465 A057466

KEYWORD

nonn,more

AUTHOR

Robert G. Wilson v, Sep 27 2000

EXTENSIONS

a(10)-a(15) from Nathaniel Johnston, Apr 19 2011

a(16)-a(17) from Joerg Arndt, Apr 28 2012

STATUS

approved

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Last modified February 22 07:46 EST 2020. Contains 332118 sequences. (Running on oeis4.)