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

1,2

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

Prog

(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];

Crossrefs

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

Sequence in context: A366384 A291761 A319337 * A305891 A319347 A318888

Adjacent sequences: A373247 A373248 A373249 * A373251 A373252 A373253

Keyword

nonn

Author

Antti Karttunen, May 30 2024

Status

approved