Thursday 9 June 2011

Explore a number of strange

Tweeted Benjamin Vitale (@ binvitali) to follow people, 203 203^2 + 203^0 + 203^3 = 8406637 to Twitter and Nr.

Alex bogomolni (@ kotthiknotmath) and note that n=abc if (s) and then abc^a+abc^b+abc^c may abc agents of the a, b, c =0not one.

Search quick calculation (using ™ math) n=d_k\ldots d_0 \leq 10000 gives the following numbers (base 10 numbers) that n^{d_k}+\ldots +n^{d_0} is Prime:

10, 20, 230, 203, 308, 309, 330, 350, 503, 550, 650, 960, 1068, 1110, 1206, 1350, 1404, 1480, 5.30, 1802, 1860, 1910, 2032, 2038, 2044, 2054, 2250, and, 2502, 3044, 3082, 3541, 3,974, 4032, 4046, 4072, 4120, 4340, 4450th, 4540, 4650, 4908, 5174, 5310, 5402, 5231, 5770, 5820, 6038, 6100, 6120, 6206, 7039, 6520, 6830, 8065, 8074, 7110 State trading, 8120, 8333, 8446, 8610, 8690, 8902, 8,960, 9064, 9330, 9402, 9408, 9950

How to increase these numbers?

They become relatively rare?

Let's V(p) denote the number n=d_k \ldots d_0 \textrm{ (base 10 digits) } \leq p to n^{d_k}+\ldots + n^{d_0} is prime.

How \frac{V (p)}{p} can break with increasing pdiffer?

Here is a plot to break this p=200000: up to

\frac{V(p)}{p} \to 0 Seems as p increases, although the decline exaggerated highly forishortinade plot.

Do \frac{V(p)}{p} \to 0 k p over?

Matt Henderson (@ mattthen2) gave the following comment useful:

Let Z(p) indicates n\leq p number of containing 0 figures.

Then k>1for everyone.

Because V(p)\leq Z(p) p view for all that:

\frac{V(10^n)}{10^{nk}}\to 0\textrm{ as } n\to \inftyk>1To all.

Tagged as: initial Setup

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