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

1,2

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.

Links

Table of n, a(n) for n=1..86.

Example

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.

Prog

(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

Crossrefs

Cf. A005384, A066753.

Sequence in context: A176088 A069566 A336314 * A005730 A112284 A167401

Adjacent sequences: A066815 A066816 A066817 * A066819 A066820 A066821

Keyword

nonn

Author

Joseph L. Pe, Jan 19 2002

Extensions

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

Status

approved