A323909 Balanced ternary representation of A004718, Per Nørgård's "infinity sequence".

0, 1, 2, 5, 1, 0, 7, 3, 2, 5, 0, 1, 5, 2, 6, 4, 1, 0, 7, 3, 0, 1, 2, 5, 7, 3, 1, 0, 3, 7, 8, 17, 2, 5, 0, 1, 5, 2, 6, 4, 0, 1, 2, 5, 1, 0, 7, 3, 5, 2, 6, 4, 2, 5, 0, 1, 6, 4, 5, 2, 4, 6, 22, 15, 1, 0, 7, 3, 0, 1, 2, 5, 7, 3, 1, 0, 3, 7, 8, 17, 0, 1, 2, 5, 1, 0, 7, 3, 2, 5, 0, 1, 5, 2, 6, 4, 7, 3, 1, 0, 3, 7, 8, 17, 1, 0

Offset: 0

Author

Antti Karttunen, Feb 10 2019

Keywords

• nonn

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

Crossrefs

Cf. A004718, A083866 (positions of zeros), A117966, A117967, A117968, A323907 (rgs-transform), A323908.

Programs

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); }; \\ After 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)); };

Formula

If A004718(n) >= 0, then a(n) = A117967(A004718(n)), otherwise a(n) = A117968(-A004718(n)).

For all n >= 1, A117966(a(n)) = A004718(n).