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Continued fraction for Niven's constant.
4

%I #20 Jul 04 2024 15:15:56

%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 (decimal expansion).

%K nonn,cofr

%O 0,3

%A _Eric W. Weisstein_

%E Offset changed by _Andrew Howroyd_, Jul 04 2024