A340820 Decimal expansion of (1 + Product_{p prime} (1 - 2/(p*(p+1))))/2.

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

Offset: 0

Author

Amiram Eldar, Jan 22 2021

Keywords

• nonn
• cons

Comments

The asymptotic density of numbers k such that A046660(k) is even (A162644).

Detrey et al. (2016) calculated 1000 decimal digits of this constant.

Examples

			0.735840306806498934037617816540241043712963191003493...
		

Links

• Jérémie Detrey, Pierre-Jean Spaenlehauer and Paul Zimmermann, Computing the rho constant, 2016.
• Michael J. Mossinghoff and Timothy S. Trudgian, A tale of two omegas, arXiv:1906.02847 [math.NT], 2019. See page 9.

Crossrefs

Cf. A013661, A046660, A065472, A162644, A340818, A340819.

Programs

PARI

(prodeulerrat(1 - 2/(p*(p+1))) + 1)/2

Formula

Equals (1 + A065472/zeta(2))/2.

Equals lim_{n->oo} A340818(n)/A340819(n).