The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A057486 Numbers k such that x^k + x^m + 1 is factorable over GF(2) for all m between 1 and k. 5
 8, 13, 16, 19, 24, 26, 27, 32, 37, 38, 40, 43, 45, 48, 50, 51, 53, 56, 59, 61, 64, 67, 69, 70, 72, 75, 77, 78, 80, 82, 83, 85, 88, 91, 96, 99, 101, 104, 107, 109, 112, 114, 115, 116, 117, 120, 122, 125, 128, 131, 133, 136, 138, 139, 141, 143, 144, 149, 152, 157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Brent, Hart, Kruppa, and Zimmermann found that 57885161 is a term of this sequence. - Charles R Greathouse IV, May 30 2013 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..5000 (first 200 terms from T. D. Noe) Richard Brent, The Software gf2x. Paul Zimmermann, There is no primitive trinomial of degree 57885161 over GF(2), posting to NMBRTHRY mailing list [alternate link] Index entries for sequences related to trinomials over GF(2) EXAMPLE a(1) = 8 because x^8 + x^1 + 1 = (1 + x + x^2)*(1 + x^2 + x^3 + x^5 + x^6), x^8 + x^2 + 1 = (1 + x + x^4)^2, x^8 + x^3 + 1 = (1 + x + x^3)*(1 + x + x^2 + x^3 + x^5), x^8 + x^4 + 1 = (1 + x + x^2)^4, x^8 + x^5 + 1 = (1 + x^2 + x^3)*(1 + x^2 + x^3 + x^4 + x^5), x^8 + x^6 + 1 = (1 + x^3 + x^4)^2, and x^8 + x^7 + 1 = (1 + x + x^2)*(1 + x + x^3 + x^4 + x^6). MATHEMATICA Do[ k = 1; While[ ToString[ Factor[ x^n + x^k + 1, Modulus -> 2 ]] != ToString[ x^n + x^k + 1 ] && k < n, k++ ]; If[ k == n, Print[ n ]], {n, 2, 234} ] PROG (PARI) is(n)=for(s=1, n\2, if(polisirreducible((x^n+x^s+1)*Mod(1, 2)), return(0))); 1 \\ Charles R Greathouse IV, May 30 2013 CROSSREFS Complement of A073571. Cf. A001153, A002475, A073639. Sequence in context: A328241 A287159 A272486 * A188198 A129410 A338598 Adjacent sequences: A057483 A057484 A057485 * A057487 A057488 A057489 KEYWORD nonn AUTHOR Robert G. Wilson v, Sep 28 2000 STATUS approved

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

Last modified July 24 23:57 EDT 2024. Contains 374585 sequences. (Running on oeis4.)