A336473 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A329697(i) = A329697(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jul 24 2020

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of the ordered pair [A278222(n), A329697(n)].

For all i, j: A336460(i) = A336460(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A278222, A329697.

Cf. also A286622, A336394, A336460, A336470, A336471, A336472, A336474.

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 };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
Aux336473(n) = [A278222(n), A329697(n)];
v336473 = rgs_transform(vector(up_to, n, Aux336473(n)));
A336473(n) = v336473[n];