login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%I #14 Jul 05 2024 15:18:21

%S 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,

%T 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,

%U 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

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

%t digits = 93;

%t $MaxExtraPrecision = 4 digits;

%t terms = 4 digits;

%t LR = Join[{0, 0, 0}, LinearRecurrence[{-2, -1, 1, 1}, {-3, 4, -5, 3}, terms + 10]];

%t r[n_Integer] := LR[[n]];

%t c = Exp[NSum[r[n] PrimeZetaP[n - 1]/(n - 1), {n, 4, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]];

%t ContinuedFraction[c][[;; digits]] (* _Jean-François Alcover_, Aug 01 2019 *)

%o (PARI) contfrac(prodeulerrat(1 - 1/(p^2*(p+1)))) \\ _Amiram Eldar_, Mar 14 2021

%Y Cf. A065465 (decimal expansion).

%K nonn,cofr

%O 0,3

%A _Benoit Cloitre_, Dec 02 2002

%E Offset changed by _Andrew Howroyd_, Jul 05 2024