A351955 Lexicographically earliest infinite sequence such that a(i) = a(j) => A328571(A108951(i)) = A328571(A108951(j)) for all i, j >= 1.

1, 2, 3, 2, 4, 3, 5, 6, 7, 4, 8, 3, 9, 5, 4, 6, 10, 7, 11, 4, 5, 8, 12, 7, 13, 9, 14, 5, 15, 13, 16, 17, 8, 10, 18, 7, 19, 11, 9, 13, 20, 18, 21, 8, 13, 12, 22, 7, 23, 13, 10, 9, 24, 14, 25, 5, 11, 15, 26, 13, 27, 16, 18, 17, 28, 8, 29, 10, 12, 18, 30, 31, 32, 19, 33, 11, 25, 9, 34, 13, 31, 20, 35, 18, 36, 21, 15, 8

Offset: 1

Author

Antti Karttunen, Apr 03 2022

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of A346091, or equally, of A346093.

For all i, j:

a(i) = a(j) => A006530(i) = A006530(j) [equally, A061395(i) = A061395(j)],

a(i) = a(j) => A329040(i) = A329040(j) => A351956(i) = A351956(j),

a(i) = a(j) => A329343(i) = A329343(j).

Interestingly, some of the rays in the scatter plot appear to be cut to discontinuous segments.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A108951, A328571, A346091, A346093.

Cf. also A006530, A061395, A329040, A329343, A351956, and A286621, A329045, A329345, A344594.

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; };
A002110(n) = prod(i=1,n,prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) };
A328571(n) = { my(m=1, p=2); while(n, m *= (p^!!(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A346091(n) = A328571(A108951(n));
v351955 = rgs_transform(vector(up_to, n, A346091(n)));
A351955(n) = v351955[n];