A365388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A334867(i) = A334867(i) and A365386(j) = A365386(j) for all i, j >= 1.

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 31, 16, 32, 1, 33, 17, 34, 9, 35, 18, 36, 5, 37, 19, 38, 10, 39, 20, 40, 3, 41, 21, 42, 11, 43, 22, 44, 6, 45, 23, 46, 12, 47, 24, 48, 2, 49, 25, 41

Offset: 1

Author

Antti Karttunen, Sep 07 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A334867(n), A365386(n)], or equally, of the quadruplet [A329697(n), A334204(n), A331410(n), A365385(n)].

For all i, j:

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

a(i) = a(j) => A334867(i) = A334867(j),

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

a(i) = a(j) => A365386(i) = A365386(j).

Links

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

Crossrefs

Cf. A163511, A329697, A331410, A334204, A334867, A335880, A365385, A365386.

Differs from A003602 and A351090 for the first time at n=99, where a(99) = 41, while A003602(99) = A351090(99) = 50.

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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A334204(n) = A329697(A163511(n));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
A365385(n) = A331410(A163511(n));
A365388aux(n) = [A329697(n),A334204(n),A331410(n),A365385(n)];
v365388 = rgs_transform(vector(up_to,n,A365388aux(n)));
A365388(n) = v365388[n];