A366293 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365711(i) = A365711(j) for all i, j >= 1, where A365711 is the Dirichlet inverse of balanced ternary enumeration of integers (A117966).

1, 1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 8, 9, 10, 11, 11, 12, 5, 13, 5, 14, 15, 16, 8, 17, 9, 5, 18, 19, 20, 21, 22, 23, 24, 21, 5, 25, 26, 27, 28, 29, 30, 31, 32, 5, 12, 33, 34, 34, 28, 17, 35, 6, 5, 36, 37, 38, 39, 40, 5, 41, 21, 5, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 25, 51, 52, 4, 27, 53, 5, 5, 54, 55, 56, 57, 58, 59, 60, 61, 5

Offset: 1

Author

Antti Karttunen, Oct 06 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of A365711.

For all i, j: a(i) = a(j) => A365428(i) = A365428(j) => A359377(i) = A359377(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..59049

Crossrefs

Cf. A117966, A359377, A365428, A365711.

Programs

PARI

up_to = 3^10;
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(dA117966(n) = subst(Pol(apply(x->if(x == 2, -1, x), digits(n, 3)), 'x), 'x, 3); \\ From A117966
v366293 = rgs_transform(DirInverseCorrect(vector(up_to,n,A117966(n))));
A366293(n) = v366293[n];