A344784 Decimal expansion of the sum of the reciprocals of the prime factors of Fermat numbers (A023394).

5, 9, 7, 6, 4, 0, 4, 7, 5, 8

Offset: 0

Author

Amiram Eldar, May 28 2021

Keywords

• nonn
• cons
• more

Comments

Golomb (1955) asked if this series is convergent. Křížek et al. (2002) proved its convergence.

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

Examples

			0.5976404758...
		

References

• Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, Section 1.37, p. 248.

Links

• Steven R. Finch, Fermat Numbers and Elite Primes, preprint, 2013.
• Solomon W. Golomb, Sets of primes with intermediate density, Math. Scand., Vol. 3 (1955), pp. 264-274; alternative link.
• Michal Křížek, Florian Luca and Lawrence Somer, 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.

Crossrefs

Cf. A000215, A023394.

Formula

Equals Sum_{k>=1} 1/A023394(k).