A340552 Decimal expansion of Product_{primes p == 5, 7, 11 (mod 12)} 1/(1 - 1/p^2).

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

Offset: 0

Author

Peter Luschny, Jan 19 2021

Keywords

• nonn
• cons

Examples

			1.0883369352683420526735775059570250699813408669621752843542802162845...
		

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

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]]

Formula

A340552^(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.