The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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. = 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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