A369050 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1, and for n>1, f(n) = [A003415(n), A369049(n)], for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 56, 57, 2, 58, 59, 60, 2, 61, 62, 63, 64, 65, 2, 66, 37

Offset: 1

Author

Antti Karttunen, Jan 15 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the function f defined as: f(1) = 1, and for n>1, f(n) = [A003415(n), A369049(n)].

For all i, j:

A305800(i) = A305800(j) => a(i) = a(j),

a(i) = a(j) => A344025(i) = A344025(j) => A369051(i) = A369051(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A003415, A369049.

Cf. also A305800, A328767, A344025, A369051.

Differs from A351260 for the first time at n=77, where a(77) = 56, while A351260(77) = 47.

Differs from A300833 for the first time at n=91, where a(91) = 37, while A300833(91) = 67.

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369049(n) = (n % A003415(n));
Aux369050(n) = if(1==n,1,[A003415(n), A369049(n)]);
v369050 = rgs_transform(vector(up_to, n, Aux369050(n)));
A369050(n) = v369050[n];