A336394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A331410(i) = A331410(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Aug 10 2020

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of the ordered pair [A278222(n), A331410(n)].

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A003602, A278222, A324400, A331410, A336392.

Cf. also A286622, A336473.

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));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux336394(n) = [A278222(n), A331410(n)];
v336394 = rgs_transform(vector(up_to, n, Aux336394(n)));
A336394(n) = v336394[n];