A340565 Decimal expansion of the Product_{lesser twin primes p == 5 (mod 6)} 1/(1 - 1/p^2).

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

Offset

1,3

Comments

Lesser twin primes A001359 (with the exception of the first prime, 3) are congruent to 5 mod 6: this constant is smaller than A340576.

By extrapolating method most probably the next two decimal digits are 1.056932291(46).

The known high-precision algorithms for Euler products are based on the Dirichlet L function and the Moebius inversion formula (see Mathematica procedure of Jean-François Alcover in A175646).

The constant is between 1.056932291453... and 1.056932291494. - R. J. Mathar, Feb 14 2025

Links

Table of n, a(n) for n=1..11.

Example

1.0569322914...

Crossrefs

Cf. A005596, A065463, A065465, A065483, A065485, A065489, A065493, A072691, A082695, A111003, A175646.

Sequence in context: A230461 A277522 A019598 * A197283 A244843 A118261

Adjacent sequences: A340562 A340563 A340564 * A340566 A340567 A340568

Keyword

nonn,cons,hard,more

Author

Artur Jasinski, Jan 11 2021

Extensions

One more digit confirmed by a bracketing of partial products - R. J. Mathar, Feb 14 2025

Status

approved