cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A216845 Numbers n such that the polynomial 1 + x + x^2 + x^3 + x^4 + ... + x^(n-1) is reducible over GF(2).

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%I A216845 #36 Dec 07 2012 15:43:11
%S A216845 4,6,7,8,9,10,12,14,15,16,17,18,20,21,22,23,24,25,26,27,28,30,31,32,
%T A216845 33,34,35,36,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,54,55,56,57,
%U A216845 58,60,62,63,64,65,66,68,69,70,71,72,73,74,75,76,77,78,79
%N A216845 Numbers n such that the polynomial 1 + x + x^2 + x^3 + x^4 + ... + x^(n-1) is reducible over GF(2).
%C A216845 Alternately, the union of the composite numbers and the primes for which 2 is not a primitive root.
%C A216845 This is the complement of A001122 (primes for which 2 is a primitive root). - _V. Raman_, Dec 01 2012
%t A216845 reducibleQ[n_] := Module[{f = FactorList[Sum[x^i, {i, 0, n - 1}], Modulus -> 2]}, Length[f] > 2 || f[[2, 2]] > 1]; Select[Range[2, 100], reducibleQ] (* _T. D. Noe_, Sep 19 2012 *)
%o A216845 (PARI) for(i=4, 100, if(isprime(i), if(znorder(Mod(2, i))!=(i-1), print(i)), print(i))) \\ _V. Raman_, Oct 14 2012
%o A216845 (PARI) is(n)=n>3 && (!isprime(n) || znorder(Mod(2,n))<n-1) \\ _Charles R Greathouse IV_, Oct 16 2012
%Y A216845 Cf. A002326, A001122, A216838.
%K A216845 nonn
%O A216845 1,1
%A A216845 _V. Raman_, Sep 17 2012