A365395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365427(i) = A365427(j) for all i, j >= 0.

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

Offset: 0

Author

Antti Karttunen, Sep 04 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A365425(n), A365427(n)].

Restricted growth sequence transform of the function f(n) = A336390(A163511(n)).

For all i, j: a(i) = a(j) => A365385(i) = A365385(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A000265, A003602, A046523, A163511, A336390, A365385, A365425, A365427, A365394.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A365425(n) = A046523(A000265(A163511(n)));
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
A365427(n) = A336467(A163511(n));
A365395aux(n) = [A365425(n), A365427(n)];
v365395 = rgs_transform(vector(1+up_to,n,A365395aux(n-1)));
A365395(n) = v365395[1+n];

Formula

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).