Sequence of numbers which follow a rule
This is a rare case where the comment is absolutely necessary, along the lines of

/* The sequence is Fibonacci numbers modulo 10. It is periodic with a
   period of 60. Each even digits appears for 4 times, and each odd
   digit for 8 times, per period. The sum of primes per period is 128.

           Reviewer's note: are you sure? Looks like you consider 1 as prime.

   To get the desired results, compute the number of entire periods,
   and process the last incomplete part separately. */



Rename subSequences toperiods
Collapse the switch to

kFound = ((k &amp; 0x01)? 8: 4) * periods;

I don't see how kFound can be 1 or 2, so

if(( kFound == 1 ) || ( kFound == 2 )) kFound++;


seems to serve no purpose. Correct me if I am wrong.
Working with the incomplete part should be split into functions. Precompute the period once, and pass it to separate functions (computing sum of primes, counting occurrences, and returning number at position).