A033151 Continued fraction for Niven's constant.

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, 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, 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

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn
• cofr

Links

• I. Niven, Averages of Exponents in Factoring Integers, Proc. Amer. Math. Soc. 22, 356-360, 1969.
• Eric Weisstein's World of Mathematics, Niven's Constant
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A033150 (decimal expansion).

Programs

Mathematica

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 *)

Extensions

Offset changed by Andrew Howroyd, Jul 04 2024