A341355 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1 and for n > 1, f(n) = [A341353(n), A341353(2*n)].

1, 2, 3, 4, 5, 3, 3, 2, 4, 6, 2, 3, 3, 3, 2, 4, 2, 7, 3, 2, 6, 4, 7, 3, 4, 3, 3, 3, 3, 4, 2, 5, 2, 4, 3, 8, 3, 3, 4, 4, 2, 2, 3, 7, 5, 8, 5, 3, 4, 2, 5, 3, 3, 3, 6, 3, 4, 3, 2, 2, 3, 4, 3, 6, 3, 4, 2, 2, 2, 3, 3, 2, 5, 3, 3, 3, 9, 2, 3, 2, 4, 4, 2, 4, 4, 3, 8, 8, 3, 6, 6, 2, 2, 6, 3, 3, 2, 5, 2, 4, 3, 6, 9, 3, 4

Offset: 1

Author

Antti Karttunen, Feb 14 2021

Keywords

• nonn

Comments

For all i, j: a(i) = a(j) => A329903(i) = A329903(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A007949, A156552, A329903, A341353, A341354.

Cf. also A331304, A340680.

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; };
A007949(n) = valuation(n,3);
A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A341353(n) = A007949(A156552(n));
Aux341355(n) = if(1==n,1, [A341353(n), A341353(2*n)]);
v341355 = rgs_transform(vector(up_to, n, Aux341355(n)));
A341355(n) = v341355[n];