cp's OEIS Frontend

A366794 Binary encoding of the twos (-1's) in the balanced ternary representation of Per Nørgård's "infinity sequence".

%I A366794 #13 Oct 24 2023 11:47:45
%S A366794 0,0,1,1,0,0,2,0,1,1,0,0,1,1,2,0,0,0,2,0,0,0,1,1,2,0,0,0,0,2,3,3,1,1,
%T A366794 0,0,1,1,2,0,0,0,1,1,0,0,2,0,1,1,2,0,1,1,0,0,2,0,1,1,0,2,4,2,0,0,2,0,
%U A366794 0,0,1,1,2,0,0,0,0,2,3,3,0,0,1,1,0,0,2,0,1,1,0,0,1,1,2,0,2,0,0,0,0,2,3,3,0,0
%N A366794 Binary encoding of the twos (-1's) in the balanced ternary representation of Per Nørgård's "infinity sequence".
%C A366794 The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.
%H A366794 Antti Karttunen, <a href="/A366794/b366794.txt">Table of n, a(n) for n = 0..65536</a>
%H A366794 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A366794 a(n) = A289814(A323909(n)).
%e A366794 A004718(254) = -7. In balanced ternary representation (see A117966) this is represented as -1*9 + 1*3 + -1*1. Taking the negative coefficients, and converting them to a binary string gives "101", which in base-2 (A007088) is equal to 5, therefore a(254) = 5.
%o A366794 (PARI)
%o A366794 up_to = 65536;
%o A366794 A004718list(up_to) = { my(v=vector(up_to)); v[1]=1; v[2]=-1; for(n=3, up_to, v[n] = if(n%2, 1+v[n>>1], -v[n/2])); (v); }; \\ From the code in A004718.
%o A366794 v004718 = A004718list(up_to);
%o A366794 A004718(n) = if(!n,n,v004718[n]);
%o A366794 A117967(n) = if(n<=1,n,if(!(n%3),3*A117967(n/3),if(1==(n%3),1+3*A117967((n-1)/3),2+3*A117967((n+1)/3))));
%o A366794 A117968(n) = if(1==n,2,if(!(n%3),3*A117968(n/3),if(1==(n%3),2+3*A117968((n-1)/3),1+3*A117968((n+1)/3))));
%o A366794 A323909(n) = { my(x = A004718(n)); if(x >= 0,A117967(x),A117968(-x)); };
%o A366794 A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
%o A366794 A366794(n) = A289814(A323909(n));
%Y A366794 Cf. A004718, A007088, A117966, A289814, A323909, A366793.
%K A366794 nonn
%O A366794 0,7
%A A366794 _Antti Karttunen_, Oct 24 2023