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

1,2

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

Table of n, a(n) for n=1..18.

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.

Formula

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

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 *)

Crossrefs

Cf. A033150, A033151, A000009, A000010.

Sequence in context: A320037 A122664 A318649 * A009306 A324555 A318969

Adjacent sequences: A033149 A033150 A033151 * A033153 A033154 A033155

Keyword

nonn,more

Author

Eric W. Weisstein

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

Status

approved