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
Keywords
Examples
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.
Links
Programs
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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));
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