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

0,1

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.

Links

Table of n, a(n) for n=0..14.

Formula

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

Example

0.215967949902374...

Prog

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

Crossrefs

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

Sequence in context: A349635 A176665 A199050 * A193629 A021467 A011132

Adjacent sequences: A306536 A306537 A306538 * A306540 A306541 A306542

Keyword

nonn,cons,more

Author

Dimitris Valianatos, Feb 22 2019

Status

approved