\(14\) and \(197\) are somewhat special numbers. How?

\(14:\) Number of digits in \(14\) is \(2\). Trying to make a

*n-onacci*sequence with \(n=2\) \[1,4,(1+4=)5,(4+5=)9,(5+9=)14...\] Thus, 14 lies in*2-onacci*sequence started from its digits.**197:**Number of digits in \(197\) is \(3\). Repeating the above steps with \(n=3\), \[1,9,7,(1+9+7=)17,(9+7+17=)33,(7+17+33=)57 \\ ,(17+33+57=)107,(33+57+107)=197...\] Thus, 197 lies in*3-onacci*sequence started from its digits.

Such special numbers are called *Keith Numbers*, with \(14\) being the smallest number that satisfy such property.

Calculate the sum of the 20th and 40th Keith Numbers.

**Details and Assumptions**:

\(\text{n-onacci}\) is a name given by me only.

\(\text{Fibonacci sequence}\) is an example of

*2-onacci*sequence starting with \([0,1]\).\(\text{Tribonacci sequence}\) is an example of

*3-onacci*sequence starting with \([0,0,1]\).

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