A Keith number (or repfigit, for "repetitive Fibonacci-like digit") works like this: take the digits of \(n\) as the seed of a sequence where each new term is the sum of the previous \(k\) terms (\(k\) = digit count). If the sequence lands exactly on \(n\), it's a Keith number.
For 197: start 1, 9, 7 → 17 → 33 → 57 → 107 → 197. ✓
Keith numbers are remarkably scarce — fewer than 100 are known below \(10^{19}\), and finding them requires brute-force search. Mike Keith introduced them in 1987. It is not known whether infinitely many exist, though heuristics suggest about \(\frac{9}{10}\log_{10} 2 \approx 0.9\) of them per order of magnitude.