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 A107220 Numbers n such that 1 + (x + x^3 + x^5 + x^7 + ...+ x^(2*n+1)) is irreducible over GF(2). 0
 1, 3, 5, 7, 9, 13, 23, 27, 31, 37, 63, 69, 117, 119, 173, 219, 223, 247, 307, 363, 383, 495, 695, 987, 2519, 3919, 4633, 6537, 8881, 12841, 15935, 16383, 16519, 26525, 34415, 95139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All terms are odd as irreducible polynomials over GF(2) necessarily have an odd number of nonzero coefficients. Next term > 10^5. - Joerg Arndt, Apr 28 2012 LINKS Joerg Arndt, Matters Computational (The Fxtbook), section 40.9.10 "Irreducible alternating polynomials", pp.853 N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references) EXAMPLE The number 5 is in the sequence because x^11 + x^9 + x^7 + x^5 + x^3 + x + 1 is irreducible over GF(2) (and 11 = 2*5 + 1). PROG (PARI) forstep(d=1, 10^5, 2, p=(1+sum(t=0, d, x^(2*t+1))); if(polisirreducible(Mod(1, 2)*p), print1(d, ", "))); (Sage) p = 1; P. = GF(2)[] for n in range(1, 10^5, 2):     p = p + x^(2*(n-1)+1) + x^(2*n+1);     if p.is_irreducible():         print(n) # Joerg Arndt, Apr 28 2012 CROSSREFS Sequence in context: A262602 A133847 A134180 * A249412 A098758 A275254 Adjacent sequences:  A107217 A107218 A107219 * A107221 A107222 A107223 KEYWORD nonn,hard,more AUTHOR Joerg Arndt, Jun 08 2005 EXTENSIONS More terms from Joerg Arndt, Apr 02 2011 and (terms >=2519), Apr 27 2012 STATUS approved

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Last modified September 19 02:37 EDT 2019. Contains 327186 sequences. (Running on oeis4.)