A323907 Lexicographically earliest positive sequence such that a(i) = a(j) => A004718(i) = A004718(j), for all i, j >= 0.

1, 2, 3, 4, 2, 1, 5, 6, 3, 4, 1, 2, 4, 3, 7, 8, 2, 1, 5, 6, 1, 2, 3, 4, 5, 6, 2, 1, 6, 5, 9, 10, 3, 4, 1, 2, 4, 3, 7, 8, 1, 2, 3, 4, 2, 1, 5, 6, 4, 3, 7, 8, 3, 4, 1, 2, 7, 8, 4, 3, 8, 7, 11, 12, 2, 1, 5, 6, 1, 2, 3, 4, 5, 6, 2, 1, 6, 5, 9, 10, 1, 2, 3, 4, 2, 1, 5, 6, 3, 4, 1, 2, 4, 3, 7, 8, 5, 6, 2, 1, 6, 5, 9, 10, 2, 1

Offset: 0

Author

Antti Karttunen, Feb 09 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of A004718, Per Nørgård's "infinity sequence".

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..65535

Crossrefs

Restricted growth sequence transform of A004718, A323908 and A323909.

Cf. A083866 (positions of ones).

Programs

PARI

up_to = 65535;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
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]);
v323907 = rgs_transform(vector(1+up_to,n,A004718(n-1)));
A323907(n) = v323907[1+n];