Kata

We have the following sequence:

f(0) = 0
f(1) = 1
f(2) = 1
f(3) = 2
f(4) = 4;
f(n) = f(n-1) + f(n-2) - f(n-3) + f(n-4) - f(n-5);

The first term of the sequence that has its last nine digits forms a prime number is the value, 8480150779 (total of 10 digits), and corresponds to the 92-th term, because 480150779 is prime. We can follow this observation in the next terms of the sequence and see the behaviour.

n-th term   k-th lastDig prime         term value   total digits   last9Digit    isPrime(last9Digit)
   92             1                     8480150779        10        480150779         True

   98             2                    35922495169        11        922495169         True

  110             3                   644603021049        12        603021049         True

  122             4                 11566931883761        14        931883761         True

  134             5                207560170886697        15        170886697         True

Create a function kth_lastDigPrime(), that receives the value of k as an argument and outputs, the ordinal number that corresponds to the term value and the number formed by the last nine digits. Let's see some cases:

k_thlastDigPrime(1)--------> [92, 480150779]

k_thlastDigPrime(2)--------> [98, 922495169]

k_thlastDigPrime(5)--------> [134, 170886697]

(Advise: Use a fast primality test, Miller Rabin test or similar)

Happy coding!