A078087 Continued fraction expansion of Product_{p prime} (1 - 1/(p^2*(p+1))).

0, 1, 7, 2, 3, 1, 1, 1, 7, 1, 1, 6, 1, 5, 1, 1, 3, 2, 1, 1, 3, 2, 1, 1, 1, 1, 13, 1, 16, 1, 1, 16, 1, 80, 1, 1, 1, 1, 7, 5, 1, 4, 1, 33, 3, 8, 1, 8, 1, 16, 11, 1, 2, 6, 1, 19, 1, 12, 5, 11, 1, 7, 5, 1, 1, 1, 2, 5, 1, 4, 1, 3, 4, 4, 4, 1, 11, 1, 2, 5, 4, 12, 3, 1, 4, 1, 3, 1, 168, 1, 4, 1, 1

Offset

0,3

Links

Table of n, a(n) for n=0..92.

Mathematica

digits = 93;
$MaxExtraPrecision = 4 digits;
terms = 4 digits;
LR = Join[{0, 0, 0}, LinearRecurrence[{-2, -1, 1, 1}, {-3, 4, -5, 3}, terms + 10]];
r[n_Integer] := LR[[n]];
c = Exp[NSum[r[n] PrimeZetaP[n - 1]/(n - 1), {n, 4, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]];
ContinuedFraction[c][[;; digits]] (* Jean-François Alcover, Aug 01 2019 *)

Prog

(PARI) contfrac(prodeulerrat(1 - 1/(p^2*(p+1)))) \\ Amiram Eldar, Mar 14 2021

Crossrefs

Cf. A065465 (decimal expansion).

Sequence in context: A126341 A324788 A354640 * A176976 A291361 A198607

Adjacent sequences: A078084 A078085 A078086 * A078088 A078089 A078090

Keyword

nonn,cofr

Author

Benoit Cloitre, Dec 02 2002

Extensions

Offset changed by Andrew Howroyd, Jul 05 2024

Status

approved