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

1,3

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.

Links

Table of n, a(n) for n=1..85.

Example

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.

Prog

(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

Crossrefs

Cf. A018252, A066753.

Sequence in context: A190185 A331189 A176123 * A326142 A028284 A359169

Adjacent sequences: A066802 A066803 A066804 * A066806 A066807 A066808

Keyword

nonn

Author

Joseph L. Pe, Jan 19 2002

Extensions

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

Status

approved