determine the following products:
A) describe the pattern(s) you see.
1 x 142857, 2 x 142857, 3 x 142857.
B) do more computations until you can predict the next product.
Do you have a calculator? Then do what it says:
1 x 142857 = 142857
2 x 142857 = 285714
3 x 142857 = 428571
B) do more computations until you can predict the next product.
Do what it says:
4 x 142857 = 571428
5 x 142857 = 714285
6 x 142857 = 857142
7 x 142857 = 999999
C) along the "what if" theme, this pattern seems to break at 7 X 142857. continue to find and write products of 142857 and 8,9,10, etc. what patterns do you see now.
8 x 142857 = 1142856
9 x 142857 = 1285713
10 x 142857 = 1428570
11 x 142857 = 1571427
12 x 142857 = 1714284
13 x 142857 = 1857141
On all those we have have a 1 in front, followed by 1 less
than the numbers in the first batch. Then
we have another break in the pattern at 14, which puts a
1 in front of 1 lest than the 999999 encountered at the
last break.
14 x 142857 = 1999998
Then we have
15 x 142857 = 2142855
16 x 142857 = 2285712
17 x 142857 = 2428569
18 x 142857 = 2571426
19 x 142857 = 2714283
20 x 142857 = 2857140
On all those we have have a 2 in front, followed by 2 less
than the numbers in the first batch. Then we have another
break from the pattern at 21:
21 x 142857 = 2999997
If we keep on we'll have a break at every multiple of 7 which
will add one to the 1st digit of the last break, followed by
1 more less than the numbers in the first batch.
Edwin