A378096 Decimal expansion of Product_{k>=2} (1 - 1/A047233(k)^2).

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

Offset

0,1

Comments

Infinite product (1-1/((q-1)^2)) where q = 5, 7, 11, 13, 17, 19, ... (A007310), are integers of the form sqrt(24*k+1), where k are terms of A001318.

Links

Table of n, a(n) for n=0..104.

Formula

Equals 2^(2/3)*sqrt(3)/Pi. - Amiram Eldar, Nov 17 2024

Example

0.87518006857301813466054083008273947043287617439849...

Mathematica

RealDigits[2^(2/3)*Sqrt[3]/Pi, 10, 120][[1]] (* Amiram Eldar, Nov 17 2024 *)

Crossrefs

Cf. A001318, A007310, A047233.

Sequence in context: A076417 A114137 A185346 * A200017 A316728 A231098

Adjacent sequences: A378093 A378094 A378095 * A378097 A378098 A378099

Keyword

cons,nonn

Author

Frank Richter, Nov 16 2024

Status

approved