A366886 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366885(i) = A366885(j) for all i, j >= 0.

1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 3, 1, 16, 9, 17, 5, 18, 10, 19, 3, 20, 11, 21, 6, 22, 12, 23, 2, 24, 13, 25, 7, 26, 14, 27, 4, 27, 15, 13, 8, 14, 3, 28, 1, 29, 16, 30, 9, 31, 17, 32, 5, 33, 18, 34, 10, 35, 19, 36, 3, 37, 20, 38, 11, 39, 21, 40, 6

Offset: 0

Author

Antti Karttunen, Nov 04 2023

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of A366885.

Albeit quite ugly, the scatter plot is still interesting. - Antti Karttunen, Jan 03 2024

Links

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

Crossrefs

Cf. A163511, A347385, A366885.

Cf. also A366806, A366881, A366891 (compare the scatter plots).

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));
A347385(n) = if(1==n,n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
A366885(n) = A347385(A163511(n));
v366886 = rgs_transform(vector(1+up_to,n,A366885(n-1)));
A366886(n) = v366886[1+n];