A331372 Decimal expansion of Sum_{k>=1} 1/(2^k - 3).

3, 4, 3, 6, 7, 3, 4, 3, 3, 1, 8, 1, 7, 6, 9, 0, 1, 8, 5, 4, 4, 4, 8, 2, 8, 3, 3, 3, 8, 1, 2, 4, 1, 2, 0, 6, 1, 8, 8, 8, 0, 7, 1, 7, 6, 4, 8, 6, 7, 8, 3, 8, 4, 8, 6, 5, 1, 1, 0, 5, 9, 2, 1, 7, 4, 5, 5, 0, 0, 9, 5, 4, 1, 2, 4, 1, 8, 0, 9, 7, 4, 9, 5, 2, 6, 7, 8

Offset: 0

Author

Amiram Eldar, May 03 2020

Keywords

• nonn
• cons

Comments

Erdős and Graham (1980) asked whether this constant is irrational, and Borwein (1991) proved that it is indeed irrational.

Examples

			0.34367343318176901854448283338124120618880717648678...
		

References

• Paul Erdős, Some of my favourite unsolved problems, in A. Baker, B. Bollobás and A. Hajnal (eds.), A tribute to Paul Erdős, Cambridge University Press, 1990, p. 470.

Links

• Peter B. Borwein, On the irrationality of Sigma (1/(q^n + r)), Journal of Number Theory, Vol. 37, No. 3 (1991), pp. 253-259.
• Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, L'enseignement Mathématique, Université de Genève, 1980, p. 62.

Crossrefs

Cf. A036563 (2^n-3), A065442.

Programs

Mathematica

RealDigits[Sum[1/(2^k - 3), {k, 1, 400}], 10, 100][[1]]

PARI

suminf(k=1, 1/(2^k - 3)) \\ Michel Marcus, May 03 2020