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

0,1

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).

References

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

Links

Table of n, a(n) for n=0..9.

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.

Formula

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

Example

0.5976404758...

Crossrefs

Cf. A000215, A023394.

Sequence in context: A349161 A125650 A171540 * A220261 A365238 A195285

Adjacent sequences: A344781 A344782 A344783 * A344785 A344786 A344787

Keyword

nonn,cons,more,changed

Author

Amiram Eldar, May 28 2021

Status

approved