A066818 a(n) is the least k such that n + Sum_{i=1..k} A005384(i) is prime; or 0 if none exists.

1, 2, 1, 12, 1, 2, 3, 2, 1, 4, 1, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 4, 5, 2, 7, 2, 1, 6, 1, 6, 3, 2, 3, 6, 1, 2, 3, 2, 1, 4, 1, 2, 3, 8, 1, 4, 11, 2, 3, 4, 1, 4, 5, 2, 13, 2, 1, 4, 1, 8, 3, 2, 3, 6, 1, 2, 7, 2, 1, 10, 1, 8, 3, 2, 15, 4, 1, 2, 3, 4, 1, 4, 5, 2, 7, 4

Offset: 1

Author

Joseph L. Pe, Jan 19 2002

Keywords

• nonn

Comments

There is some empirical evidence to suggest a(n) is nonzero for every n. That is, every n can be expressed as the difference between a prime and a partial sum of the Sophie Germain primes series. See A066753 for a similar conjecture.

Examples

			7 + (2 + 3 + 5) = 17, a prime and three consecutive Sophie Germain primes starting from 2, the first Sophie Germain prime, are needed to achieve this. So a(7) = 3.
		

Crossrefs

Cf. A005384, A066753.

Programs

PARI

a(n) = my(p=0, s=n); for(k=1, oo, until(isprime(2*p+1), p=nextprime(p+1)); if(isprime(s+=p), return(k))); \\ Jinyuan Wang, Jul 30 2020

Extensions

a(53) corrected by and more terms from Jinyuan Wang, Jul 30 2020