A336313 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A336125(i)) = A278222(A336125(j)) for all i, j >= 1.

1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 4, 3, 2, 2, 2, 3, 3, 2, 2, 5, 2, 2, 3, 3, 2, 2, 2, 3, 4, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2, 5, 2, 2, 4, 5, 2, 2, 2, 3, 3, 3, 2, 5, 2, 2, 3, 3, 3, 2, 2, 3, 6, 2, 2, 5, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 5, 2, 2, 4, 3, 2, 2, 2, 3, 3

Offset: 1

Author

Antti Karttunen, Jul 17 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of A278222(A336125(n)).

For all i, j: A336311(i) = A336311(j) => a(i) = a(j) => A336123(i) = A336123(j).

Links

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

Crossrefs

Cf. A253553, A278222, A336124, A336125.

Cf. also A292585, A336311, A336312, A336123.

Programs

PARI

\\ Needs also code from A336124:
up_to = 1024; \\ 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; };
A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
A336125(n) = if(n<=2,n-1,(1==A336124(n))+(2*A336125(A253553(n))));
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));
v336313 = rgs_transform(vector(up_to,n,A278222(A336125(n))));
A336313(n) = v336313[n];