A324657 a(n) is the number of successive primorials A002110(i) larger than prime(n) that need to be tried before sum prime(n)+A002110(i) is found to be composite.

0, 0, 1, 1, 1, 2, 2, 0, 3, 4, 2, 0, 5, 0, 2, 1, 1, 3, 3, 2, 5, 0, 3, 0, 1, 2, 1, 4, 0, 0, 2, 0, 2, 1, 2, 0, 3, 2, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 2, 1, 2, 3, 0, 0, 0, 1, 0, 0, 1, 4, 0, 1, 2, 0, 0, 0, 4, 1, 1, 1, 0, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 1, 0, 2, 1, 0, 1, 0, 0, 2, 4, 2, 1, 0, 0, 3, 0, 4, 1, 3, 0, 0, 1, 0

Offset: 1

Author

Antti Karttunen, Mar 11 2019

Keywords

• nonn

Comments

See comments and examples in A324656.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25000
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000040, A002110, A324656.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A235224(n, p=2) = if(!n, n, 1+A235224(n\p, nextprime(p+1)));
A324656(n) = { my(k=0,b=A235224(n)); while(isprime(n+A002110(b+k)), k++); (k); };
A324657(n) = A324656(prime(n));

Formula

a(n) = A324656(A000040(n)).