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

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, 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, 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

Offset

0,7

Comments

The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65536

Index entries for sequences related to binary expansion of n

Formula

a(n) = A289814(A323909(n)).

Example

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.

Prog

(PARI)
up_to = 65536;
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.
v004718 = A004718list(up_to);
A004718(n) = if(!n, n, v004718[n]);
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))));
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))));
A323909(n) = { my(x = A004718(n)); if(x >= 0, A117967(x), A117968(-x)); };
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
A366794(n) = A289814(A323909(n));

Crossrefs

Cf. A004718, A007088, A117966, A289814, A323909, A366793.

Sequence in context: A376847 A261812 A077266 * A214302 A129561 A259895

Adjacent sequences: A366791 A366792 A366793 * A366795 A366796 A366797

Keyword

nonn

Author

Antti Karttunen, Oct 24 2023

Status

approved