login
A328317
Smallest prime not dividing A328316(n), with a(0) = 1 by convention; Equally, for n > 0, smallest prime dividing A328316(1+n).
11
1, 2, 3, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2
OFFSET
0,2
COMMENTS
a(2n+1) = 2 for all n >= 0. Does the pattern of 5's in the even bisection also continue?
FORMULA
a(0) = 1; and for n > 0, a(n) = A053669(A328316(n)).
a(n) = A020639(A328316(1+n)).
For n >= 1, a(n) = A326810(A328316(n-1)). - Antti Karttunen, Nov 15 2019
PROG
(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328316(n) = if(!n, 0, A276086(A328316(n-1)));
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A328317(n) = if(0==n, 1, A053669(A328316(n)));
\\ Or alternatively as:
A020639(n)=if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1)
A328317(n) = A020639(A328316(1+n));
KEYWORD
nonn,hard,more
AUTHOR
Antti Karttunen, Oct 14 2019
EXTENSIONS
a(12)-a(13) from Jinyuan Wang, Jul 20 2020
STATUS
approved