login
Decimal expansion of sum of reciprocals of cousin primes.
6

%I #23 Feb 16 2025 08:33:15

%S 1,1,9,7,0,4,4,9

%N Decimal expansion of sum of reciprocals of cousin primes.

%C The value is obtained by summing cousin prime pairs with values less than 2^42 (which yields 1.10633...) and a logarithmic extrapolation of Brun's constant A065421.

%C The estimate by [Park-Lee] is 1.197054+-7e-6. - _R. J. Mathar_, Feb 09 2013

%D Yeonyong Park, Heonsoo Lee, On the several differences between primes, J. Appl. Math. & Computing 13 (2003) vol 1-2, pp 37-51.

%H Prime Curios!, <a href="https://t5k.org/curios/page.php/1.1970449.html">Sum of reciprocals of cousin primes</a>

%H Marek Wolf, <a href="https://citeseerx.ist.psu.edu/pdf/efa69289aa31f0260e0b603e951b0e25bd875fae">On the Twin and Cousin Primes</a>, (1996) IFTUWr 909/96

%H Marek Wolf, <a href="https://citeseerx.ist.psu.edu/pdf/e8b77670ea186507fac861e110b50e0d8643c98c">Generalized Brun's constants</a>, (1997) IFTUWr 910/97

%H Eric E. Weisstein, <a href="https://mathworld.wolfram.com/CousinPrimes.html">MathWorld: Cousin primes</a>

%F Equals 1.1970449... = (1/7+1/11)+(1/13+1/17)+.. = Sum_{n>=2} (1/A023200(n) + 1/A046132(n)).

%K nonn,cons,more,changed

%O 1,3

%A _Kausthub Gudipati_, Aug 15 2011