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A305418 Permutation of nonnegative integers: a(1) = 0, a(2n) = 1 + 2*a(n), a(2n+1) = 2*a(A305422(2n+1)).

%I A305418 #11 Jun 10 2018 21:14:33
%S A305418 0,1,2,3,6,5,4,7,10,13,8,11,16,9,14,15,30,21,32,27,12,17,34,23,64,33,
%T A305418 22,19,18,29,128,31,258,61,36,43,256,65,38,55,512,25,130,35,46,69,
%U A305418 1024,47,20,129,62,67,66,45,2048,39,70,37,4096,59,8192,257,26,63,54,517,16384,123,24,73,16386,87,32768,513,142,131,8194,77,132,111,48,1025,42,51
%N A305418 Permutation of nonnegative integers: a(1) = 0, a(2n) = 1 + 2*a(n), a(2n+1) = 2*a(A305422(2n+1)).
%C A305418 This is GF(2)[X] analog of A156552. Note the indexing: the domain starts from 1, while the range includes also zero.
%H A305418 Antti Karttunen, <a href="/A305418/b305418.txt">Table of n, a(n) for n = 1..4096</a>
%H A305418 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A305418 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A305418 a(1) = 0, a(2n) = 1 + 2*a(n), a(2n+1) = 2*a(A305422(2n+1)).
%F A305418 a(n) = A054429(A305428(n)).
%F A305418 For all n >= 1:
%F A305418 A000120(a(n)) = A091222(n).
%F A305418 A069010(a(n)) = A091221(n).
%F A305418 A106737(a(n)) = A091220(n).
%F A305418 A132971(a(n)) = A091219(n).
%F A305418 A085357(a(n)) = A304109(n).
%o A305418 (PARI)
%o A305418 A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
%o A305418 A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k));
%o A305418 A305422(n) = { my(f = subst(lift(factor(Pol(binary(n))*Mod(1, 2))),x,2)); for(i=1,#f~,f[i,1] = Pol(binary(A305419(f[i,1])))); fromdigits(Vec(factorback(f))%2,2); };
%o A305418 A305418(n) = if(1==n,(n-1),if(!(n%2),1+(2*(A305418(n/2))),2*A305418(A305422(n))));
%Y A305418 Cf. A305417 (inverse).
%Y A305418 Cf. A305422.
%Y A305418 Cf. also A091203, A156552, A052331, A305428.
%K A305418 nonn
%O A305418 1,3
%A A305418 _Antti Karttunen_, Jun 10 2018