Definition:Stolarsky-Harborth Constant

Definition

The Stolarsky-Harborth constant is the lower bound for the number $\beta$ defined as:

$\beta > \dfrac {P_n} {n^{\lg 3} }$

where:

$P_n$ is the number of odd elements in the first $n$ rows of Pascal's triangle

$\lg 3$ denotes the logarithm base $2$ of $3$.

Its value is given by:

$\beta \approx 0 \cdotp 81255 \, 65590 \, 160063 \, 8769 \ldots$

This sequence is A077464 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

• Bounds on Number of Odd Terms in Pascal's Triangle

Source of Name

This entry was named for Kenneth B. Stolarsky and Heiko Harborth.

Sources

• 1977: Heiko Harborth: Number of Odd Binomial Coefficients (Proc. Amer. Math. Soc. Vol. 62: pp. 19 – 22)  www.jstor.org/stable/2041936

• 1977: Kenneth B. Stolarsky: Power and Exponential Sums of Digital Sums Related to Binomial Coefficient Parity (SIAM J. Appl. Math. Vol. 32: pp. 717 – 730)  www.jstor.org/stable/2100181

• Weisstein, Eric W. "Stolarsky-Harborth Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Stolarsky-HarborthConstant.html