cp's OEIS Frontend

A304108 Numbers n such that the (0,1)-polynomial encoded in binary expansion of n has at least one duplicated irreducible divisor when the factorization is done in polynomial ring GF(2)[X].

%I A304108 #9 May 13 2018 20:44:56
%S A304108 4,5,8,10,12,15,16,17,20,21,24,27,28,30,32,34,36,39,40,42,44,45,48,51,
%T A304108 52,54,56,57,60,63,64,65,68,69,72,75,76,78,80,81,84,85,88,90,92,95,96,
%U A304108 99,100,102,104,105,107,108,112,114,116,119,120,124,125,126,128,130,132,135,136,138,140,141,144,147,148,150,151,152,153,156,160,162
%N A304108 Numbers n such that the (0,1)-polynomial encoded in binary expansion of n has at least one duplicated irreducible divisor when the factorization is done in polynomial ring GF(2)[X].
%C A304108 Positions of zeros in A091219 and A304109. Numbers n such that A091221(n) < A091222(n).
%H A304108 Antti Karttunen, <a href="/A304108/b304108.txt">Table of n, a(n) for n = 1..32768</a>
%H A304108 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%e A304108 4 is present as 4 = A048720(2,2) = A048720(A014580(1), A014580(1)).
%e A304108 5 is present as 5 = A048720(3,3) = A048720(A014580(2), A014580(2)).
%e A304108 10 is present as 10 = A048720(2,A048720(3,3)).
%o A304108 (PARI)
%o A304108 isA304108(n) = { my(fm=factor(Pol(binary(n))*Mod(1, 2))); for(k=1, #fm~, if(fm[k, 2] > 1, return(1))); (0); };
%o A304108 k=0; n=0; while(k<100, n++; if(isA304108(n), k++; print1(n,", ")));
%Y A304108 Cf. A304107 (complement).
%Y A304108 Cf. A014580, A048720, A091219, A091221, A091222, A304109.
%Y A304108 Cf. also A013929.
%K A304108 nonn
%O A304108 1,1
%A A304108 _Antti Karttunen_, May 13 2018