A340551 Decimal expansion of 1 / Product_{primes p == 5, 7, 11 (mod 12)} 1/(1 - 1/p^2).

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

Offset: 0

Author

Peter Luschny, Jan 18 2021

Keywords

• nonn
• cons

Examples

			0.9188330999291487244256631507533988473271937061440690243133487417135896...
		

Links

• Salma Ettahri, Olivier Ramaré, and Léon Surel, Fast multi-precision computation of some Euler products, arXiv:1908.06808 [math.NT], 2019.
• Étienne Fouvry, Claude Levesque, and Michel Waldschmidt, Representation of integers by cyclotomic binary forms, arXiv:1712.09019 [math.NT], 2017 and Acta Arithmetica, online 15 March 2018.

Crossrefs

Cf. A301430.

Programs

Mathematica

(* Using Vaclav Kotesovec's function Z from A301430. *)
$MaxExtraPrecision = 1000; digits = 90;
digitize[c_] := RealDigits[Chop[N[c, digits]], 10, digits - 1][[1]];
digitize[(Z[12, 5, 2] Z[12, 7, 2] Z[12, 11, 2])^(-1)]

Formula

A340551^(-1/2) = A301430 / (3^(1/4)*Pi^(1/2)*log(2+sqrt(3))^(1/4)/(2^(5/4)* Gamma(1/4))), see É. Fouvry et al.