A066868 a(n) is the least k such that n + Sum_{i=1..k} A005385(i) is prime; or 0 if none exists.

2, 1, 10, 5, 2, 1, 2, 1, 12, 5, 2, 1, 4, 1, 4, 5, 2, 1, 2, 3, 4, 7, 12, 1, 2, 1, 4, 7, 2, 3, 2, 1, 4, 5, 2, 1, 4, 1, 6, 17, 2, 1, 4, 3, 6, 5, 2, 1, 2, 3, 4, 11, 12, 1, 2, 1, 4, 5, 2, 3, 2, 1, 4, 5, 14, 1, 2, 1, 10, 5, 2, 7, 10, 1, 6, 7, 2, 1, 8, 3, 4, 7, 26, 1

Offset

1,1

Comments

Conjecture: a(n) is nonzero for all n, so every n can be represented as the difference between a prime and a partial sum of the safe primes series. See A066753 for a similar conjecture.

Links

Table of n, a(n) for n=1..84.

Example

4 + (5 + 7 + 11 + 23 + 47) = 97, a prime and 5 consecutive safe primes, starting from the first safe prime 5, are needed to achieve this. Hence a(4) = 5.

Prog

(PARI) a(n) = my(p=3, s=n); for(k=1, oo, until(isprime((p-1)/2), p=nextprime(p+1)); if(isprime(s+=p), return(k))); \\ Jinyuan Wang, Jul 30 2020

Crossrefs

Cf. A005385, A066753.

Sequence in context: A126450 A235608 A112333 * A193900 A319373 A143172

Adjacent sequences: A066865 A066866 A066867 * A066869 A066870 A066871

Keyword

nonn,less

Author

Joseph L. Pe, Jan 21 2002

Extensions

Offset changed to 1 by Jinyuan Wang, Jul 30 2020

Status

approved