mixedmath

Explorations in math and programming
David Lowry-Duda



While idly thinking while heading back from the office, and then more later while thinking after dinner with my academic little brother Alex Walker and my future academic little sister-in-law Sara Schulz, we began to think about $2017$, the number.

General Patterns

Counting to 20

$$\begin{array}{ll} 1 = 2\cdot 0 + 1^7 & 11 = 2 + 0! + 1 + 7 \\ 2 = 2 + 0 \cdot 1 \cdot 7 & 12 = 20 - 1 - 7 = -2 + (0! + 1)\cdot 7 \\ 3 = (20 + 1)/7 = 20 - 17 & 13 = 20 - 1 \cdot 7 \\ 4 = -2 + 0 - 1 + 7 & 14 = 20 - (-1 + 7) \\ 5 = -2 + 0\cdot 1 + 7 & 15 = -2 + 0 + 17 \\ 6 = -2 + 0 + 1 + 7 & 16 = -(2^0) + 17 \\ 7 = 2^0 - 1 + 7 & 17 = 2\cdot 0 + 17 \\ 8 = 2 + 0 - 1 + 7 & 18 = 2^0 + 17 \\ 9 = 2 + 0\cdot 1 + 7 & 19 = 2\cdot 0! + 17 \\ 10 = 2 + 0 + 1 + 7 & 20 = 2 + 0! + 17. \end{array}$$

In each expression, the digits $2, 0, 1, 7$ appear, in order, with basic mathematical symbols. I wonder what the first number is that can't be nicely expressed (subjectively, of course)?

Iterative Maps on 2017

Now let's look at less-common manipulations with numbers.

A Few Matrices


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Comments (1)
  1. 2017-01-22 enginist

    Sounds like a cricket match between Hardy and Ramanujan.