A328576 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)], for all i, j.

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

Offset: 0

Author

Antti Karttunen, Oct 20 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of function f, defined as: f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)].

For all i, j: a(i) = a(j) => A328114(i) = A328114(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003557, A032742, A276086, A276088, A328114, A328575, A328577.

Programs

PARI

up_to = 32768;
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; };
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };
A328575(n) = A003557(A032742(A276086(n)));
Aux328576(n) = if(!n,n,[A276088(n), A328575(n)]);
v328576 = rgs_transform(vector(1+up_to, n, Aux328576(n-1)));
A328576(n) = v328576[1+n];