A306539 Decimal expansion of Sum (1/p - 1/q) as (p, q) runs through the twin primes.

2, 1, 5, 9, 6, 7, 9, 4, 9, 9, 0, 2, 3, 7, 4

Offset: 0

Author

Dimitris Valianatos, Feb 22 2019

Keywords

• nonn
• cons
• more

Comments

If a = Sum (1/p) as (p, q) runs through the twin primes and

If b = Sum (1/q) as (p, q) runs through the twin primes, then

a + b = 1.902160583209... (Brun's constant) and

a - b = 0.215967949902374... (This constant).

So a = Sum_{n>=1} 1/A001359(n) = 1.059064266555685...

and b = Sum_{n>=1} 1/A006512(n) = 0.843096316653315... are 2 new constants for twin primes.

Examples

			0.215967949902374...
		

Crossrefs

Cf. A065421, A001359, A006512, A001097, A209328.

Programs

PARI

p=2;s=0.0;forprime(n=3,1e14,if(n-p==2,s+=(1/p-1/n));p=n;);print1(s)

Formula

Equals 2 * A209328. - Amiram Eldar, Nov 20 2020