A305434 Restricted growth sequence transform of A285713, formed from the prime signature of A245612(n).

1, 2, 2, 2, 3, 2, 4, 5, 2, 6, 3, 5, 2, 6, 2, 3, 3, 2, 6, 6, 2, 3, 3, 2, 6, 7, 2, 3, 8, 6, 2, 2, 3, 3, 9, 2, 2, 10, 3, 11, 6, 2, 12, 7, 3, 3, 9, 3, 3, 9, 2, 13, 3, 2, 6, 14, 3, 9, 2, 3, 6, 3, 6, 5, 3, 3, 12, 11, 3, 11, 3, 2, 7, 15, 3, 3, 7, 16, 2, 3, 2, 3, 3, 3, 2, 9, 3, 10, 3, 3, 6, 12, 3, 6, 3, 3, 17, 6, 3, 9, 6, 6, 2, 2, 3, 6

Offset: 0

Author

Antti Karttunen, Jun 01 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A046523, A245612, A285713.

Cf. also A305433.

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A254049(n) = A048673((2*n)-1);
A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A285713(n) = A046523(A245612(n));
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; };
v305434 = rgs_transform(vector(65538,n,A285713(n-1)));
A305434(n) = v305434[1+n];