A366893 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366892(i) = A366892(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, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 31, 16, 32, 1, 33, 17, 34, 9, 35, 18, 36, 5, 37, 19, 38, 10, 39, 20, 40, 3, 41, 21, 42, 11, 43, 22, 44, 6, 45, 23

Offset: 0

Author

Antti Karttunen, Nov 04 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of A366892.

Links

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

Crossrefs

Cf. A163511, A336652, A366892.

Cf. also A366806.

Differs from A003602 for the first time at n=121, where a(121) = 24, while A003602(121) = 61.

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));
A336652(n) = if(1==n,n,my(f=factor(n)); prod(i=1,#f~,if(2==f[i,1],1,-1+(((f[i,1]^(1+f[i,2]))-1) / (f[i,1]-1)))));
A366892(n) = A336652(A163511(n));
v366893 = rgs_transform(vector(1+up_to,n,A366892(n-1)));
A366893(n) = v366893[1+n];