A033150 Decimal expansion of Niven's constant.

1, 7, 0, 5, 2, 1, 1, 1, 4, 0, 1, 0, 5, 3, 6, 7, 7, 6, 4, 2, 8, 8, 5, 5, 1, 4, 5, 3, 4, 3, 4, 5, 0, 8, 1, 6, 0, 7, 6, 2, 0, 2, 7, 6, 5, 1, 6, 5, 3, 4, 6, 9, 0, 9, 9, 9, 9, 4, 2, 8, 4, 9, 0, 6, 5, 4, 7, 3, 1, 3, 1, 9, 2, 1, 6, 8, 1, 2, 2, 4, 9, 1, 9, 3, 4, 2, 4, 4, 1, 3, 2, 1, 0, 0, 8, 7, 1, 0, 0, 1, 7, 9

Offset

1,2

Comments

This constant is the average value of A051903. - Charles R Greathouse IV, Oct 30 2012

There are no 9's in the first 50 digits after the decimal point. Then, suddenly, it goes 909999. - Bobby Jacobs, Aug 13 2017

Named after the Canadian-American mathematician Ivan Morton Niven (1915 - 1999). - Amiram Eldar, Aug 19 2020

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 112-115.

Links

Table of n, a(n) for n=1..102.

C. W. Anderson, Problem 6015, The American Mathematical Monthly, Vol. 82, No. 2 (1975), pp. 183-184, T. Salat, Prime Decomposition of Integers, solution to Problem 6015, ibid., Vol. 83, No. 10 (1976), p. 820.

Ivan Niven, Averages of Exponents in Factoring Integers, Proc. Amer. Math. Soc., Vol. 22, No. 2 (1969), pp. 356-360.

Simon Plouffe, The Niven constant to 256 digits.

Kaneenika Sinha, Average orders of certain arithmetical functions, Journal of the Ramanujan Mathematical Society, Vol. 21, No. 3 (2006), pp. 267-277.

Eric Weisstein's World of Mathematics, Niven's Constant.

Wikipedia, Niven's constant.

Formula

Equals 1 + Sum_{j>=2} 1-(1/zeta(j)).

Equals 1 - Sum_{k>=2} mu(k)/(k*(k-1)), where mu is the Möbius function (A008683) (Anderson, 1975; Sinha, 2006). - Amiram Eldar, Aug 19 2020

Example

1.7052111401...

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++]; rd[n] (* Jean-François Alcover, Oct 25 2012 *)

Prog

(PARI) 1+suminf(j=2, 1-1/zeta(j)) \\ Charles R Greathouse IV, Aug 13 2017

Crossrefs

Cf. A008683, A033151, A033152, A033153, A033154.

Sequence in context: A099737 A271177 A299624 * A064648 A116198 A137915

Adjacent sequences: A033147 A033148 A033149 * A033151 A033152 A033153

Keyword

nonn,cons

Author

Eric W. Weisstein

Extensions

Offset corrected by Oleg Marichev (oleg(AT)wolfram.com), Jan 28 2008

Status

approved