A286622 -id:A286622 - cp's OEIS frontend

A361020 Lexicographically earliest infinite sequence such that a(i) = a(j) => A343029(i) = A343029(j) and A343030(i) = A343030(j) for all i, j >= 0.

1, 2, 3, 4, 2, 5, 6, 7, 3, 4, 5, 8, 4, 9, 10, 11, 2, 5, 6, 7, 5, 8, 9, 12, 6, 7, 8, 13, 7, 14, 15, 16, 3, 4, 5, 8, 4, 9, 10, 11, 5, 8, 9, 12, 8, 13, 14, 17, 4, 9, 10, 11, 9, 12, 13, 18, 10, 11, 12, 19, 11, 20, 21, 22, 2, 5, 6, 7, 5, 8, 9, 12, 6, 7, 8, 13, 7, 14, 15, 16, 5, 8, 9, 12, 8, 13, 14, 17, 9, 12, 13, 18, 12, 19, 20, 23, 6, 7, 8

Offset: 0

Antti Karttunen, Mar 03 2023

Restricted growth sequence transform of the ordered pair [A343029(n), A343030(n)].
For all i, j >= 0:
  a(i) = a(j) => A000120(i) = A000120(j),
  a(i) = a(j) => A004718(i) = A004718(j) => A361016(i) = A361016(j).
Because the Danish composer Per Nørgård's "infinity sequence" (A004718) can be represented as an difference A343029(n) - A343030(n), it is a function of this sequence, whose scatter plot shows interesting structure. (The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.)

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A343029, A343030.
Cf. A000120, A004718, A361016.
Cf. also A286622.

up_to = 65537;
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; };
A343029(n) = { my(t=1, ret=0); for(i=0, if(n, logint(n, 2)), if(bittest(n, i), ret+=t, t=!t)); ret; }; \\ From A343029
A343030(n) = { my(t=0, ret=0); for(i=0, if(n, logint(n, 2)), if(bittest(n, i), ret+=t, t=!t)); ret; }; \\ From A343030
Aux361020(n) = [A343029(n), A343030(n)];
v361020 = rgs_transform(vector(1+up_to,n,Aux361020(n-1)));
A361020(n) = v361020[1+n];

cp's OEIS Frontend

A361020 Lexicographically earliest infinite sequence such that a(i) = a(j) => A343029(i) = A343029(j) and A343030(i) = A343030(j) for all i, j >= 0.

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