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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).
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 06 2023
STATUS
approved