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Decimal expansion of the sum of the reciprocals of the elite primes (A102742).
1

%I #6 Aug 06 2024 11:24:27

%S 7,0,0,7,6,4,0,1,1,5

%N Decimal expansion of the sum of the reciprocals of the elite primes (A102742).

%C Křížek et al. (2002) proved that this series is convergent.

%C The first 10 terms were given by Finch (2018).

%D Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, Section 1.37, p. 247.

%H Steven R. Finch, <a href="https://citeseerx.ist.psu.edu/pdf/19649c0b982e07df575fd68a8127c6a73ee952de">Fermat Numbers and Elite Primes</a>, preprint, 2013.

%H Michal Křížek, Florian Luca and Lawrence Somer, <a href="http://dx.doi.org/10.1006/jnth.2002.2782">On the convergence of series of reciprocals of primes related to the Fermat numbers, J. Number Theory, Vol. 97, No. 1 (2002), pp. 95-112.

%F Equals Sum_{k>=1} 1/A102742(k).

%e 0.7007640115...

%Y Cf. A102742.

%K nonn,cons,more

%O 0,1

%A _Amiram Eldar_, May 28 2021