A336920 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A329697(n), A331410(n), A336158(n)], for all i, j >= 1.

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 6, 4, 7, 1, 8, 5, 9, 3, 10, 6, 11, 2, 12, 6, 13, 4, 14, 7, 15, 1, 16, 8, 16, 5, 14, 9, 16, 3, 17, 10, 18, 6, 19, 11, 20, 2, 21, 12, 22, 6, 14, 13, 23, 4, 24, 14, 25, 7, 11, 15, 26, 1, 23, 16, 25, 8, 27, 16, 18, 5, 28, 14, 29, 9, 27, 16, 18, 3, 30, 17, 9, 10, 31, 18, 32, 6, 28, 19, 27, 11, 33, 20, 32, 2, 17, 21, 34, 12, 28, 22, 9, 6, 35

Offset: 1

Author

Antti Karttunen, Aug 10 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the triplet [A329697(n), A331410(n), A336158(n)].

For all i, j:

A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),

a(i) = a(j) => A335880(i) = A335880(j),

a(i) = a(j) => A336391(i) = A336391(j),

a(i) = a(j) => A336471(i) = A336471(j).

Links

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

Crossrefs

Cf. A000265, A003602, A324400, A329697, A331410, A335880, A336391, 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));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux336920(n) = [A329697(n), A331410(n), A336158(n)];
v336920 = rgs_transform(vector(up_to, n, Aux336920(n)));
A336920(n) = v336920[n];