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A366793
Binary encoding of the ones in the balanced ternary representation of Per Nørgård's "infinity sequence".
2
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.
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); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 24 2023
STATUS
approved