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%I A048296 #28 Mar 12 2021 03:34:49
%S A048296 0,2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,2,2,4,4,2,1,6,1,1,4,2,2,1,
%T A048296 109,1,1,4,9,3,45,8,4,1,2,1,13,13,1,1,2,1,1,2,1,4,2,3,1,17,1,1,1,6,42,
%U A048296 1,3,1,1,4,1,1,1,1,1,2,4,5,4,1,26,1,1,74,1,1,2,1,2,2,1,1,10,1
%N A048296 Continued fraction for Artin's constant.
%D A048296 See A005596 for further references.
%H A048296 Harry J. Smith, <a href="/A048296/b048296.txt">Table of n, a(n) for n = 0..995</a>
%H A048296 <a href="/index/Ar#Artin">Index entries for sequences related to Artin's conjecture</a>
%e A048296 artin = 0.37395581361920228805... = 0 + 1/(2 + 1/(1 + 1/(2 + 1/(14 + ...)))). - _Harry J. Smith_, Apr 23 2009
%t A048296 digits = 105; m0 = 1000; dm = 100; Clear[s]; r[n_] := -1 + Fibonacci[n-1] + Fibonacci[n+1]; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 2, m}, NSumTerms -> m0, WorkingPrecision -> 400] // 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]; A = s[m]; ContinuedFraction[A, 93] (* _Jean-François Alcover_, Apr 15 2016 *)
%o A048296 (PARI) contfrac(prodeulerrat(1-1/(p^2-p))) \\ _Amiram Eldar_, Mar 12 2021
%Y A048296 Cf. A005596.
%K A048296 cofr,nonn,nice
%O A048296 0,2
%A A048296 _Fred Lunnon_ and _Simon Plouffe_, Dec 11 1999

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