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]
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
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 28 2000
STATUS
approved