A351452 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j) and A278222(i) = A278222(j) for all i, j >= 1.

1, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 8, 5, 9, 2, 10, 6, 11, 4, 12, 7, 13, 3, 14, 8, 15, 5, 16, 9, 17, 2, 18, 10, 19, 6, 20, 11, 21, 4, 22, 12, 23, 7, 24, 13, 25, 3, 19, 14, 26, 8, 27, 15, 28, 5, 29, 16, 30, 9, 31, 17, 32, 2, 33, 18, 34, 10, 35, 19, 36, 6, 37, 20, 24, 11, 38, 21, 39, 4, 40, 22, 41, 12, 42, 23, 43, 7, 44, 24, 45, 13, 46, 25, 47, 3, 48, 19, 49, 14, 50, 26, 51, 8, 52

Offset: 1

Author

Antti Karttunen, Feb 11 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A006530(n), A278222(n)].

For all i, j >= 1: A324400(i) = A324400(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A006530, A278222, A286622.

Cf. also A324400, A336935, A351453, A351454.

Differs from A351454 and A351460 for the first time at n=49, where a(49) = 19, while A351454(49) = A351460(49) = 26.

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; };
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
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));
Aux351452(n) = [A006530(n), A278222(n)];
v351452 = rgs_transform(vector(up_to, n, Aux351452(n)));
A351452(n) = v351452[n];