A066805 a(n) is the least k such that n + Sum_{i=1..k} A018252(i) is prime; or 0 if none exists.

1, 1, 5, 1, 6, 1, 8, 2, 5, 1, 7, 1, 5, 2, 5, 1, 7, 1, 5, 3, 6, 1, 6, 2, 5, 2, 13, 1, 6, 1, 5, 2, 5, 4, 6, 1, 8, 2, 5, 1, 6, 1, 5, 10, 5, 1, 7, 2, 8, 3, 5, 1, 7, 2, 5, 2, 7, 1, 6, 1, 5, 2, 6, 4, 6, 1, 8, 2, 5, 1, 6, 1, 5, 2, 5, 27, 7, 1, 5, 11, 5, 1, 15, 2, 5

Offset: 1

Author

Joseph L. Pe, Jan 19 2002

Keywords

• nonn

Comments

Is a(n) nonzero for all n? If so, then every n can be represented as the difference of a prime and a partial sum of the nonprime numbers series. See A066753 for a related possible representation of n as the difference of a prime and a partial sum of the prime numbers series.

Examples

			3 + (1 + 4 + 6 + 8 + 9) = 31, a prime and 5 consecutive nonprime numbers starting with 1 are required to achieve this. Hence a(3) = 5.
		

Crossrefs

Cf. A018252, A066753.

Programs

PARI

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

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 12 2002