A336391 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A336158(i) = A336158(j), for all i, j >= 1.

1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 5, 1, 6, 4, 6, 3, 7, 3, 3, 2, 8, 3, 9, 2, 10, 5, 2, 1, 5, 6, 5, 4, 10, 6, 5, 3, 6, 7, 6, 3, 11, 3, 3, 2, 4, 8, 12, 3, 10, 9, 12, 2, 12, 10, 10, 5, 3, 2, 13, 1, 12, 5, 10, 6, 5, 5, 6, 4, 14, 10, 15, 6, 5, 5, 6, 3, 16, 6, 6, 7, 17, 6, 17, 3, 14, 11, 5, 3, 7, 3, 17, 2, 6, 4, 11, 8, 14, 12, 6, 3, 18

Offset: 1

Author

Antti Karttunen, Aug 10 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A331410(n), A336158(n)].

For all i, j:

A336390(i) = A336390(j) => a(i) = a(j)

a(i) = a(j) => A336921(i) = A336921(j),

a(i) = a(j) => A336922(i) = A336922(j) => A336923(i) = A336923(j).

Links

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

Crossrefs

Cf. A331410, A336467, A336390, A336921, A336922, A336923.

Cf. also A336471.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux336391(n) = [A331410(n), A336158(n)];
v336391 = rgs_transform(vector(up_to, n, Aux336391(n)));
A336391(n) = v336391[n];