A366793 Binary encoding of the ones in the balanced ternary representation of Per Nørgård's "infinity sequence".

0, 1, 0, 2, 1, 0, 1, 2, 0, 2, 0, 1, 2, 0, 0, 3, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 2, 1, 0, 4, 0, 2, 0, 1, 2, 0, 0, 3, 0, 1, 0, 2, 1, 0, 1, 2, 2, 0, 0, 3, 0, 2, 0, 1, 0, 3, 2, 0, 3, 0, 3, 4, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 2, 1, 0, 4, 0, 1, 0, 2, 1, 0, 1, 2, 0, 2, 0, 1, 2, 0, 0, 3, 1, 2, 1, 0, 2, 1, 0, 4, 1, 0

Offset

0,4

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) = A289813(A323909(n)).

Example

A004718(254) = -7. In balanced ternary representation (see A117966) this is represented as -1*9 + 1*3 + -1*1. Taking the positive coefficients, and converting them to a binary string gives "10", which in base-2 (A007088) is equal to 2, therefore a(254) = 2.

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)); };
A289813(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); };
A366793(n) = A289813(A323909(n));

Crossrefs

Cf. A004718, A007088, A117966, A289813, A323909, A366794.

Sequence in context: A321100 A244422 A061896 * A069850 A141581 A179286

Adjacent sequences: A366790 A366791 A366792 * A366794 A366795 A366796

Keyword

nonn

Author

Antti Karttunen, Oct 24 2023

Status

approved