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%I #8 Aug 06 2024 11:22:02
%S 5,9,7,6,4,0,4,7,5,8
%N Decimal expansion of the sum of the reciprocals of the prime factors of Fermat numbers (A023394).
%C Golomb (1955) asked if this series is convergent. Křížek et al. (2002) proved its convergence.
%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. 248.
%H Steven R. Finch, <a href="https://citeseerx.ist.psu.edu/pdf/19649c0b982e07df575fd68a8127c6a73ee952de">Fermat Numbers and Elite Primes</a>, preprint, 2013.
%H Solomon W. Golomb, <a href="https://eudml.org/doc/165595">Sets of primes with intermediate density</a>, Math. Scand., Vol. 3 (1955), pp. 264-274; <a href="https://www.jstor.org/stable/24490175">alternative link</a>.
%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/A023394(k).
%e 0.5976404758...
%Y Cf. A000215, A023394.
%K nonn,cons,more
%O 0,1
%A _Amiram Eldar_, May 28 2021
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