A365386 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A365385(i) = A365385(j) for all i, j >= 1.

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 5, 4, 7, 1, 8, 5, 9, 3, 10, 6, 3, 2, 11, 5, 12, 4, 13, 7, 4, 1, 14, 8, 15, 5, 16, 9, 12, 3, 9, 10, 8, 6, 17, 3, 6, 2, 10, 11, 18, 5, 11, 12, 17, 4, 17, 13, 11, 7, 5, 4, 19, 1, 20, 14, 21, 8, 22, 15, 8, 5, 23, 16, 24, 9, 8, 12, 9, 3, 16, 9, 9, 10, 24, 8, 24, 6, 25, 17, 9, 3, 10, 6, 25

Offset: 1

Author

Antti Karttunen, Sep 03 2023

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of the ordered pair [A331410(n), A365385(n)].

For all i, j: A365388(i) = A365388(j) => a(i) = a(j) => A365387(i) = A365387(j).

Links

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

Crossrefs

Cf. A003602, A163511, A331410, A365385, A365387, A365388.

Cf. also A334867.

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));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
A365385(n) = A331410(A163511(n));
A365386aux(n) = [A331410(n),A365385(n)];
v365386 = rgs_transform(vector(up_to,n,A365386aux(n)));
A365386(n) = v365386[n];