Exclusionary Numbers

So I've been looking into a pattern regarding the addition of prime numbers, where n is the number of consecutive primes in the series (2 always being the first prime in the series), with n=3 being the lowest term in the series, represented by [2,3,5]. A range can be created when multiplying n by 2 and n by the largest prime. In this case, 6-15. There are numbers inside this series that cannot be reached by adding up n members of the nth series. For example, 14 is the only number that cannot be reached for n=3 (I call these "exclusionary numbers"). The following are the exclusionary numbers up through n=10:



n=3 : 14
n=4 : 25, 27
n=5 : 44, 48, 50, 52, 53, 54
n=6 : 69, 71, 73, 75, 77
n=7 : 102,106,108,110,112,114,116,117,118
n=8 : 137,139,141,143,145,147,149,151
n=9 : 184,188,190,192,194,196,198,200,202,204,205,206
n=10: 249,255,259,261,265,267,269,271,273,275,277,279,281,283,285,286,287,288,289

I set the first number in each series to be the result of the series, making [2,3,5]=14, [2,...,7]=25, and so on, yielding the number series:
14, 25, 44, 69, 102, 137, 184, 249...

I will be pursuing this further, as well as other properties of the exclusion series for each prime number set, especially after n=10 threw me for a loop (as was to be expected).

Prime numbers never cease to be interesting.