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%I #16 Oct 25 2017 05:11:13
%S 1,1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1,4,2,2,1,2,1,2,2,2,1,1,1,7,
%T 14,2,1,13,2,1,6,2,3,1,1,1,5,2,2,8,29,1,6,1,18,1,3,2,1,5,1,1,1,18,1,3,
%U 1,372,3,3,1,47,2,1,6,1,5,1,4,1,2,4,2,2,1,1,2,7,1,7,1,14,6,5,1,559,1
%N Continued fraction for Niven's constant.
%H I. Niven, <a href="https://doi.org/10.1090/S0002-9939-1969-0241373-5">Averages of Exponents in Factoring Integers</a>, Proc. Amer. Math. Soc. 22, 356-360, 1969.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NivensConstant.html">Niven's Constant</a>
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%t rd[n_] := rd[n] = RealDigits[ N[1 + Sum[1 - 1/Zeta[j], {j, 2, 2^n}], 105]][[1]]; rd[n = 4]; While[rd[n] =!= rd[n - 1], n++]; Niven = FromDigits[{rd[n], 1}]; ContinuedFraction[Niven, 100] (* _Jean-François Alcover_, Oct 30 2012 *)
%Y Cf. A033150.
%K nonn,cofr
%O 1,3
%A _Eric W. Weisstein_
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