This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065414 #25 Nov 27 2024 16:50:26
%S A065414 6,9,7,5,0,1,3,5,8,4,9,6,3,6,5,9,0,3,2,8,4,6,7,0,3,5,0,8,2,0,9,2,2,9,
%T A065414 2,4,0,7,3,1,5,3,9,4,6,2,1,4,5,1,5,3,9,5,3,5,4,3,7,8,7,5,2,8,8,6,4,5,
%U A065414 9,1,1,0,5,9,6,0,9,5,5,6,6,6,6,6,1,5,4,8,3,8,5,1,3,0,7,1,8,7,9
%N A065414 Decimal expansion of rank 2 Artin constant Product_{p prime} (1-1/(p^3-p^2)).
%D A065414 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.4, p. 105.
%H A065414 R. J. Mathar, <a href="http://arxiv.org/abs/0903.2514">Hardy-Littlewood constants embedded into infinite products..</a>, arxiv:0903.2514 [math.NT], 2009-2011, variable A_1^(2).
%H A065414 G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%H A065414 <a href="/index/Ar#Artin">Index entries for sequences related to Artin's conjecture</a>.
%e A065414 0.697501358496365903284670350820922924...
%t A065414 digits = 99; m0 = 1000; dm = 100; Clear[s]; r[n_] := RootSum[-1 - #^2 + #^3 &, #^n&] - 1; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 3, m}, NSumTerms -> m0, WorkingPrecision -> 300] // Exp; s[m0]; s[m = m0 + dm]; While[RealDigits[s[m], 10, digits][[1]] != RealDigits[s[m - dm], 10, digits][[1]], Print[m]; m = m + dm]; RealDigits[s[m], 10, digits][[1]] (* _Jean-François Alcover_, Apr 14 2016 *)
%o A065414 (PARI) prodeulerrat(1-1/(p^3-p^2)) \\ _Amiram Eldar_, Mar 12 2021
%Y A065414 Cf. A005596, A065417.
%K A065414 cons,nonn
%O A065414 0,1
%A A065414 _N. J. A. Sloane_, Nov 15 2001