A366382 Lexicographically earliest infinite sequence such that a(i) = a(j) => A349134(i) = A349134(j) for all i, j >= 1, where A349134 is Dirichlet inverse of Kimberling's paraphrases.

1, 2, 3, 4, 5, 6, 7, 4, 2, 8, 9, 4, 10, 11, 11, 4, 12, 1, 13, 4, 14, 15, 16, 4, 7, 17, 3, 4, 18, 7, 19, 4, 17, 20, 15, 4, 21, 22, 23, 4, 24, 25, 26, 4, 8, 27, 28, 4, 12, 11, 22, 4, 29, 6, 23, 4, 30, 31, 32, 4, 33, 34, 11, 4, 20, 10, 35, 4, 36, 9, 37, 4, 38, 39, 23, 4, 20, 40, 41, 4, 7, 42, 43, 4, 30, 44, 34, 4, 45, 5, 22

Offset: 1

Author

Antti Karttunen, Oct 12 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003602, A349134.

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; };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1])*sumdiv(n, d, if(dA003602(n) = (1+(n>>valuation(n,2)))/2;
v366382 = rgs_transform(DirInverseCorrect(vector(up_to,n,A003602(n))));
A366382(n) = v366382[n];