A334867 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A334204(i) = A334204(j) for all i, j >= 1.

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 6, 4, 6, 1, 7, 5, 8, 3, 8, 6, 9, 2, 5, 6, 8, 4, 8, 6, 10, 1, 11, 7, 9, 5, 9, 8, 12, 3, 13, 8, 14, 6, 11, 9, 15, 2, 15, 5, 13, 6, 9, 8, 9, 4, 15, 8, 16, 6, 8, 10, 17, 1, 12, 11, 14, 7, 14, 9, 18, 5, 11, 9, 19, 8, 20, 12, 21, 3, 14, 13, 12, 8, 22, 14, 21, 6, 12, 11, 14, 9, 14, 15, 15, 2, 23, 15, 14, 5, 11, 13, 12, 6, 14

Offset: 1

Author

Antti Karttunen, Jun 09 2020

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of the ordered pair [A329697(n), A334204(n)].

For all i, j:

A365388(i) = A365388(j) => a(i) = a(j) => A334873(i) = A334873(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000079 (positions of ones), A163511, A329697, A334204, A334873.

Cf. also A318310, A365386, A365388.

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A054429(n) = ((3<<#binary(n\2))-n-1);
A163511(n) = if(!n,1,A005940(1+A054429(n)));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A334204(n) = A329697(A163511(n));
A334867aux(n) = [A329697(n),A334204(n)];
v334867 = rgs_transform(vector(up_to,n,A334867aux(n)));
A334867(n) = v334867[n];