Can you identify the function depicted below?

Edit: this is actually a function over nonnegative integers with the points interpolated by straight lines. I hope this helps.

Mystery function

  • 2
    $\begingroup$ So are you looking for a mathematical function $f(x)$, or the description of something that causes it (e.g., the heart rate pattern of a llama in labor)? $\endgroup$ Oct 7, 2015 at 0:35
  • $\begingroup$ Hehe its a function $f(x)$ like you said $\endgroup$ Oct 7, 2015 at 0:37

1 Answer 1


This is A043537, the number of distinct digits in the base-10 form of n. The peaks in the first part of the graph are from the multiples of 11. After it reaches 100, there is a plateau for 102-109, then it drops for 110 and 111, and goes back up for 120. After that, the dips are for numbers with two digits the same.


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