Stolarsky-Harborth Constant
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
Let 
be the number of 1s in the Binary expression of 
. Then the number of Odd BinomialCoefficients 
where 
is 
(Glaisher 1899, Fine 1947). Thenumber of Odd elements in the first 
rows of Pascal's Triangle is
 | (1) |
, where | (2) |
 | (3) |
 | (4) |
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/stlrsky/stlrsky.html Fine, N. J. ``Binomial Coefficients Modulo a Prime.'' Amer. Math. Monthly 54, 589-592, 1947. Wolfram, S. ``Geometry of Binomial Coefficients.'' Amer. Math. Monthly 91, 566-571, 1984.
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