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

Author

Antti Karttunen, Mar 03 2023

Keywords

• nonn
• look

Comments

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.)

Links

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

Crossrefs

Cf. A343029, A343030.

Cf. A000120, A004718, A361016.

Cf. also A286622.

Programs

PARI

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];