cp's OEIS Frontend

A305428 Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A305422(2n+1)).

%I A305428 #6 Jun 10 2018 21:14:51
%S A305428 0,1,3,2,5,6,7,4,13,10,15,12,31,14,9,8,17,26,63,20,11,30,61,24,127,62,
%T A305428 25,28,29,18,255,16,509,34,59,52,511,126,57,40,1023,22,253,60,49,122,
%U A305428 2047,48,27,254,33,124,125,50,4095,56,121,58,8191,36,16383,510,21,32,41,1018,32767,68,23,118,32765,104,65535,1022,241,252,16381,114,251,80,47
%N A305428 Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A305422(2n+1)).
%C A305428 Note the indexing: the domain starts from 1, while the range includes also zero.
%C A305428 This is GF(2)[X] analog of A243071.
%H A305428 Antti Karttunen, <a href="/A305428/b305428.txt">Table of n, a(n) for n = 1..2048</a>
%H A305428 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A305428 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A305428 a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A305422(2n+1)).
%F A305428 a(n) = A054429(A305418(n)).
%o A305428 (PARI)
%o A305428 A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
%o A305428 A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k));
%o A305428 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 A305428 A305428(n) = if(n<=2,(n-1),if(!(n%2),2*A305428(n/2),1+(2*(A305428(A305422(n))))));
%Y A305428 Cf. A305427 (inverse).
%Y A305428 Cf. A305422.
%Y A305428 Cf. also A243071, A305418.
%K A305428 nonn
%O A305428 1,3
%A A305428 _Antti Karttunen_, Jun 10 2018