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

1,3

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

Prog

(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(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A117966(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];

Crossrefs

Cf. A117966, A359377, A365428, A365711.

Sequence in context: A296073 A317943 A305800 * A293442 A318470 A175501

Adjacent sequences: A366290 A366291 A366292 * A366294 A366295 A366296

Keyword

nonn

Author

Antti Karttunen, Oct 06 2023

Status

approved