OFFSET
1,2
COMMENTS
Restricted growth sequence transform of function f defined as f(n) = A278222(n) when n is a prime, otherwise -n.
After its initial term 3, Fermat primes (A019434) gives the positions of 5 in this sequence, while the Mersenne primes (A000668) are each assigned to their own singleton equivalence class.
For all i, j:
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
PROG
(PARI)
up_to = 100000;
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 };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A319705aux(n) = if(isprime(n), A278222(n), -n);
v319705 = rgs_transform(vector(up_to, n, A319705aux(n)));
A319705(n) = v319705[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 26 2018
STATUS
approved