A033152 Position of first occurrence of n in the continued fraction for Niven's constant.

0, 2, 9, 6, 46, 40, 33, 12, 139, 251, 19, 334, 37, 34, 326, 184, 199, 54

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• more

Comments

The continued fraction expansion is indexed [a_0; a_1, a_2, a_3, ...];

Next term > 500. - Michel ten Voorde Jun 14 2003

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.

Crossrefs

Cf. A033150, A033151, A000009, A000010.

Programs

Mathematica

rd[n_] := rd[n] = RealDigits[ N[1 + Sum[1 - 1/Zeta[j], {j, 2, 2^n}], 400]][[1]]; rd[n = 4]; While[rd[n] =!= rd[n-1], n++]; Niven = FromDigits[{rd[n], 1}]; A033151 = ContinuedFraction[Niven]; a[n_] := Position[A033151, n][[1, 1]]; Table[a[n], {n, 1, 18}] (* Jean-François Alcover, Oct 31 2012 *)

Formula

A033151(a(n)) = n. - Andrew Howroyd, Sep 11 2024

Extensions

More terms from Michel ten Voorde, Jun 14 2003

Terms decreased by 1 for consistency with offset change in A033151 by Andrew Howroyd, Sep 11 2024