The factors series 2^n - symbolizing life, as all forms of life grow according this mathematical formula - is linked to that number, if one looks at significant digit of each term:
it retrieves the counts (or numbers) that are before the final digit of each term for adding the next term (1 of 16 adds the term 32, which gives 33, then take the 3 adds it up to 64 which gives 67, it takes 6 which will add up with 128 = 134 and 13 to 256 etc. and we are interested only in the last significant digit of the result of the addition, which is bold in the table in the last row)
2^0 | 2^1 | 2^2 | 2^3 | 2^4 | 2^5 | 2^6 | 2^7 | 2^8 | 2^9 | 2^10 | 2^11 | 2^12 | 2^13 | 2^14 | 2^15 | 2^16 | 2^17 | 2^18 |
1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 | 2048 | 4096 | 8192 | 16384 | 32768 | 65536 | 131072 | 262144 |
0 | 0 | 0 | 0 | 0 | 1 | 3 | 6 | 13 | 26 | 53 | 107 | 215 | 431 | 862 | 1724 | 3449 | 6898 | 13797 |
1 | 2 | 4 | 8 | 16 | 33 | 67 | 134 | 269 | 538 | 1077 | 2155 | 4311 | 8623 | 17246 | 34492 | 68985 | 137970 | etc. |
1 | 2 | 4 | 8 | 6 | 3 | 7 | 4 | 9 | 8 | 7 | 5 | 1 | 3 | 6 | 2 | 5 | 0 | 1 |
we then obtain a recurrent pattern of 18 digits:
124863749875136250
invert all the numbers (the latter first, the first last):
052631578947368421
this same pattern is found in :
1/19 = 0,052631578947368421052631578947368421 ...
Note: if we add these 18 numbers of this pattern, we get 81 (we also see that 18 is the 'mirror' of 81).
0+5+2+6+3+1+5+7+8+9+4+7+3+6+8+4+2+1 = 81
Still about 19, here is the list of division of 1 to 18 by 19 (there are always the same reason, each time slightly offset, which gives the sum of 81):
1/19 | 0,0526315789473684210526315789 |
2/19 | 0,1052631578947368421052631579 |
3/19 | 0,1578947368421052631578947368 |
4/19 | 0,2105263157894736842105263158 |
5/19 | 0,2631578947368421052631578947 |
6/19 | 0,3157894736842105263157894737 |
7/19 | 0,3684210526315789473684210526 |
8/19 | 0,4210526315789473684210526316 |
9/19 | 0,4736842105263157894736842105 |
10/19 | 0,5263157894736842105263157895 |
11/19 | 0,5789473684210526315789473684 |
12/19 | 0,6315789473684210526315789474 |
13/19 | 0,6842105263157894736842105263 |
14/19 | 0,7368421052631578947368421053 |
15/19 | 0,7894736842105263157894736842 |
16/19 | 0,8421052631578947368421052632 |
17/19 | 0,8947368421052631578947368421 |
18/19 | 0,9473684210526315789473684210 |
you got an explanation here http://en.wikipedia.org/wiki/Recurring_decimal
ReplyDeleteThank you very much Kader for your kind and interesting contribution
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