A389902 Lexicographically earliest infinite sequence such that a(i) = a(j) => A343029(A025480(i)) = A343029(A025480(j)) and A343030(A025480(i)) = A343030(A025480(j)) for all i, j >= 0.

1, 1, 2, 1, 3, 2, 4, 1, 2, 3, 5, 2, 6, 4, 7, 1, 3, 2, 4, 3, 5, 5, 8, 2, 4, 6, 9, 4, 10, 7, 11, 1, 2, 3, 5, 2, 6, 4, 7, 3, 5, 5, 8, 5, 9, 8, 12, 2, 6, 4, 7, 6, 8, 9, 13, 4, 7, 10, 14, 7, 15, 11, 16, 1, 3, 2, 4, 3, 5, 5, 8, 2, 4, 6, 9, 4, 10, 7, 11, 3, 5, 5, 8, 5, 9, 8, 12, 5, 8, 9, 13, 8, 14, 12, 17, 2, 4, 6, 9, 4, 10

Offset

0,3

Comments

Restricted growth sequence transform of the ordered pair [A343029(A025480(n)), A343030(A025480(n))].

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n.

Formula

a(n) = A361020(A025480(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; };
A025480(n) = (n>>valuation(n*2+2, 2));
A343029(n) = { my(t=1, ret=0); for(i=0, if(n, logint(n, 2)), if(bittest(n, i), ret+=t, t=!t)); ret; };
A343030(n) = { my(t=0, ret=0); for(i=0, if(n, logint(n, 2)), if(bittest(n, i), ret+=t, t=!t)); ret; };
Aux389902(n) = [A343029(A025480(n)), A343030(A025480(n))];
v389902 = rgs_transform(vector(1+up_to, n, Aux389902(n-1)));
A389902(n) = v389902[1+n];

Crossrefs

Cf. A025480, A343029, A343030, A361020 (even bisection).

Cf. also A389899 for another fractalization of A361020.

Sequence in context: A290103 A156061 A225395 * A295877 A336395 A336393

Adjacent sequences: A389899 A389900 A389901 * A389903 A389904 A389905

Keyword

nonn,base

Author

Antti Karttunen, Oct 20 2025

Status

approved