A365393 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364492(i) = A364492(j) for all i, j >= 0, where A364492(n) is the denominator of n / A163511(n).

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

Offset: 0

Author

Antti Karttunen, Sep 06 2023

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of A364492.

Question: Which sets of numbers cause the finite branches that grow off-angle from the rays emanating from the origin in the scatter plot, and why the sudden bends in some of them? Compare also to the scatter plot of A365431.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A000265, A003602, A163511, A364255, A364492.

Cf. also A365384, A365431.

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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A364492(n) = { my(u=A163511(n)); (u/gcd(n, u)); };
v365393 = rgs_transform(vector(1+up_to,n,A364492(n-1)));
A365393(n) = v365393[1+n];

Formula

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).