Re: [math-fun] Beastly number problem

i blathered:

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A beastly number (A051003) is a number with substring 666.

It is easy enough to prove that for each positive integer n, there is an integer k such that kn is beastly. Let f(n) be the smallest such k.

Show that f(n) is bounded over all integers n. What is the largest possible value of f(n)?

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to get the largest value of f(n) that occurs, i found it easier to consider final digits and split it into numerous cases; perhaps there is an easier calculation using initial digits.

or maybe not. let g(n) denote the smallest positive integer k , such that kn begins with the digits 666 . what is the largest value of the function g(n) ? mike