A328317 Smallest prime not dividing A328316(n), with a(0) = 1 by convention; Equally, for n > 0, smallest prime dividing A328316(1+n).

1, 2, 3, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2

Offset: 0

Author

Antti Karttunen, Oct 14 2019

Keywords

• nonn
• hard
• more

Comments

a(2n+1) = 2 for all n >= 0. Does the pattern of 5's in the even bisection also continue?

Crossrefs

Cf. A020639, A053669, A276086, A326810, A328316, A328318, A328319, A328322, A328323, A328585, A328586, A328633.

Programs

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));

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

Extensions

a(12)-a(13) from Jinyuan Wang, Jul 20 2020