“Niven's Constant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Niven's Constant

释义

Niven's Constant

N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.

Given a Positive Integer , let its Prime Factorization be written

(1)

Define the functions

and

, and

			(2)
			(3)

Then

(4)

(5)

where

is the Riemann Zeta Function (Niven 1969). Niven (1969) also proved that

(6)

where

(7)

(Sloane's A033150).

The A033151). Thepositions at which the digits 1, 2, ... first occur in the Continued Fraction are 1, 3, 10, 7, 47, 41, 34, 13, 140,252, 20, ... (Sloane's A033152). The sequence of largest terms in the Continued Fraction is 1, 2, 4, 8, 11, 14, 29,372, 559, ... (Sloane's A033153), which occur at positions 1, 3, 7, 13, 20, 35, 51, 68, 96, ... (Sloane's A033154).
References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/niven/niven.html

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 41, 1983.

Niven, I. ``Averages of Exponents in Factoring Integers.'' Proc. Amer. Math. Soc. 22, 356-360, 1969.

Plouffe, S. ``The Niven Constant.'' http://www.lacim.uqam.ca/piDATA/niven.txt.

Sloane, N. J. A. Sequences A033150,A033151,A033152,A033153, andA033154in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

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