A328498 Decimal expansion of Sum_{(p, q) runs through the twin primes} ((p mod 4) - 2) * (1/p + 1/q).

1, 8, 3, 5, 0, 0, 3, 8

Offset: 0

Author

Dimitris Valianatos, Oct 17 2019

Keywords

• nonn
• cons
• more

Comments

Because Viggo Brun's constant is 1.90216058... it is easy to find these 2 new constants:

(1/3 + 1/5) + (1/11 + 1/13) + (1/59 + 1/61) + (1/71 + 1/73) + ... = 1.04283048...

(1/5 + 1/7) + (1/17 + 1/19) + (1/29 + 1/31) + (1/41 + 1/43) + ... = 0.85933010...

Examples

			(1/3 + 1/5) - (1/5 + 1/7) + (1/11 + 1/13) - (1/17 + 1/19) - (1/29 + 1/31) + ... = 0.183500386... +- 0.000000002
		

Crossrefs

Cf. A001359, A006512, A065421.

Programs

PARI

my(p = 3, s = 0.0); forprime(n = 5, 10^16, if(n-p == 2, if(p%4 == 3, s+= 1/p + 1/n, s+= -1/p - 1/n)); p = n); s