A373250 Lexicographically earliest infinite sequence such that a(i) = a(j) => A181819(i) = A181819(j) and i mod A181819(i) = j mod A181819(j), for all i, j >= 1, where A181819 is the prime shadow of n.

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

Offset: 1

Author

Antti Karttunen, May 30 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A181819(n), A373247(n)].

For all i, j:

A373251(i) = A373251(j) => a(i) = a(j),

a(i) = a(j) => A101296(i) = A101296(j),

a(i) = a(j) => A373246(i) = A373246(j),

a(i) = a(j) => A373249(i) = A373249(j),

a(i) = a(j) => A353566(i) = A353566(j).

Links

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

Crossrefs

Cf. A101296, A181819, A353566, A373246, A373247, A373249, A373251.

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; };
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
Aux373250(n) = [A181819(n), n%A181819(n)];
v373250 = rgs_transform(vector(up_to, n, Aux373250(n)));
A373250(n) = v373250[n];