%I #21 Sep 12 2024 01:49:02

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

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

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

%C Next term > 500. - _Michel ten Voorde_ Jun 14 2003

%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>.

%F A033151(a(n)) = n. - _Andrew Howroyd_, Sep 11 2024

%t 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 *)

%Y Cf. A033150, A033151, A000009, A000010.

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_

%E More terms from _Michel ten Voorde_, Jun 14 2003

%E Terms decreased by 1 for consistency with offset change in A033151 by _Andrew Howroyd_, Sep 11 2024