A361020 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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

PROG

(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];

CROSSREFS

Cf. A343029, A343030.

Cf. A000120, A004718, A361016.

Cf. also A286622.

Sequence in context: A026346 A340791 A369422 * A368693 A333235 A295887

Adjacent sequences: A361017 A361018 A361019 * A361021 A361022 A361023

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Mar 03 2023

STATUS

approved