A336311 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A336120(i)) = A278222(A336120(j)) and A278222(A336125(i)) = A278222(A336125(j)) for all i, j >= 1.

1, 2, 2, 3, 2, 3, 2, 4, 5, 3, 2, 4, 2, 3, 5, 6, 2, 7, 2, 4, 5, 3, 2, 6, 3, 3, 8, 4, 2, 7, 2, 9, 5, 3, 3, 10, 2, 3, 5, 6, 2, 7, 2, 4, 8, 3, 2, 9, 5, 4, 5, 4, 2, 11, 3, 6, 5, 3, 2, 10, 2, 3, 8, 12, 3, 7, 2, 4, 5, 4, 2, 13, 2, 3, 4, 4, 5, 7, 2, 9, 14, 3, 2, 10, 3, 3, 5, 6, 2, 11, 5, 4, 5, 3, 3, 12, 2, 7, 8, 6, 2, 7, 2, 6, 4

Offset: 1

Author

Antti Karttunen, Jul 17 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A336312(n), A336313(n)].

For all i, j:

A305800(i) = A305800(j) => a(i) = a(j) => A001222(i) = A001222(j).

Links

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

Crossrefs

Cf. A001222, A278222, A336120, A336124, A336125.

Cf. also A292584, A305800, A336312, A336313.

Programs

PARI

\\ Needs also code from A336120, A336124, A336125, etc:
up_to = 1024;
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 }; \\ From A005940
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));
Aux336311(n) = [A278222(A336120(n)),A278222(A336125(n))];
v336311 = rgs_transform(vector(up_to,n,Aux336311(n)));
A336311(n) = v336311[n];