Here is a rule (which works in English, but perhaps in no other language) to recover the desired sequence: 0=zero, 1=one, 2=two, 3=three, 4=four, 5=five, 6=six, 7=seven, 8=eight, 9=nine. Now rearrange in inverse alphabetical order: zero=0, two=2, three=3, six=6, seven=7, one=1, nine=9, four=4, five=5, eight=8.
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The Fibonacci Series is a sequence of numbers produced by adding the last two numbers to get the next. It arbitrarily starts with 0, 1. The first few terms are: 0, 1, 1, 2, 3, 5, 8, 13 ... after 0, 1 these are generated by 0+1=1 1+1=2 2+1=3 2+3=5 3+5=8
It is almost the Fibonacci sequence, which is 0 1 1 2 3 5 8 13 21 34 55 ...1 + 2 = 32 + 3 = 53 + 5 = 85 + 8 = 13So, the sequence is 1 2 3 5 8 13
The pattern for the sequence 0 0 1 3 6 is that each term is obtained by adding the previous term multiplied by its position in the sequence (starting from 1). In other words, the nth term is given by n*(n-1)/2.
The next four number in the sequence are... 4,5,5 & 6