Tight upper and lower bounds for the reciprocal sum of Proth primes

@article{Borsos2022TightUA,
  title={Tight upper and lower bounds for the reciprocal sum of Proth primes},
  author={Bertalan Borsos and Attila Kov{\'a}cs and Norbert Tihanyi},
  journal={The Ramanujan Journal},
  year={2022}
}
Computing the reciprocal sum of sparse integer sequences with tight upper and lower bounds is far from trivial. In the case of Carmichael numbers or twin primes even the first decimal digit is unknown. For accurate bounds the exact structure of the sequences needs to be unfolded. In this paper we present explicit bounds for the sum of reciprocals of Proth primes with nine decimal digit precision. We show closed formulae for calculating the nth Proth number $$F_n$$ F n , the number of… 

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