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wasoxygen - Python, pasted on May 19: 
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import math

strCandidate = '8'
for i in range(1, 50):
   strCandidate = '9' + strCandidate
   print '(10^' + str(len(strCandidate)) + ' - 2) % 19 = ' + str(int(strCandidate) % 19)


Output: 
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(10^2 - 2) % 19 = 3
(10^3 - 2) % 19 = 10
(10^4 - 2) % 19 = 4
(10^5 - 2) % 19 = 1
(10^6 - 2) % 19 = 9
(10^7 - 2) % 19 = 13
(10^8 - 2) % 19 = 15
(10^9 - 2) % 19 = 16
(10^10 - 2) % 19 = 7
(10^11 - 2) % 19 = 12
(10^12 - 2) % 19 = 5
(10^13 - 2) % 19 = 11
(10^14 - 2) % 19 = 14
(10^15 - 2) % 19 = 6
(10^16 - 2) % 19 = 2
(10^17 - 2) % 19 = 0
(10^18 - 2) % 19 = 18
(10^19 - 2) % 19 = 8
(10^20 - 2) % 19 = 3
(10^21 - 2) % 19 = 10
(10^22 - 2) % 19 = 4
(10^23 - 2) % 19 = 1
(10^24 - 2) % 19 = 9
(10^25 - 2) % 19 = 13
(10^26 - 2) % 19 = 15
(10^27 - 2) % 19 = 16
(10^28 - 2) % 19 = 7
(10^29 - 2) % 19 = 12
(10^30 - 2) % 19 = 5
(10^31 - 2) % 19 = 11
(10^32 - 2) % 19 = 14
(10^33 - 2) % 19 = 6
(10^34 - 2) % 19 = 2
(10^35 - 2) % 19 = 0
(10^36 - 2) % 19 = 18
(10^37 - 2) % 19 = 8
(10^38 - 2) % 19 = 3
(10^39 - 2) % 19 = 10
(10^40 - 2) % 19 = 4
(10^41 - 2) % 19 = 1
(10^42 - 2) % 19 = 9
(10^43 - 2) % 19 = 13
(10^44 - 2) % 19 = 15
(10^45 - 2) % 19 = 16
(10^46 - 2) % 19 = 7
(10^47 - 2) % 19 = 12
(10^48 - 2) % 19 = 5
(10^49 - 2) % 19 = 11
(10^50 - 2) % 19 = 14


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