A373595 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n<=3) = n, f(p) = 0 for primes p > 3, and for composite n, f(n) = [A007949(n), A373591(n), A373592(n)].

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

Offset: 1

Author

Antti Karttunen, Jun 13 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the function f given in the definition.

For all i, j > 1:

A305900(i) = A305900(j) => A373594(i) = A373594(j) => a(i) = a(j),

A373593(i) = A373593(j) => a(i) = a(j),

a(i) = a(j) => b(i) = b(j), where b can be (but is not limited to) any of the sequences listed at the crossrefs-section, under "some of the matched sequences".

Links

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

Crossrefs

Cf. A007949, A373591, A373592.

Cf. A305900, A373593, A373594.

Some of the matched sequences (see comments): A001222, A359430, A369643, A369658, A373371, A373383, A373474, A373491, A373493, A373585, A373588, A373596.

Programs

PARI

up_to = 100000;
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; };
A007949(n) = valuation(n,3);
A373591(n) = sum(i=1, #n=factor(n)~, (1==n[1, i]%3)*n[2, i]);
A373592(n) = sum(i=1, #n=factor(n)~, (2==n[1, i]%3)*n[2, i]);
Aux373595(n) = if(n<=3, n, if(isprime(n), 0, [A007949(n), A373591(n), A373592(n)]));
v373595 = rgs_transform(vector(up_to, n, Aux373595(n)));
A373595(n) = v373595[n];