Integer Sequences

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Repeating Integer Sequences:
Suppose the first four terms of a sequence are 1, 9, 8 and 2.
Now each susequent term is obtained by taking the last digit of the sum of the four previous terms.
So we get: 1+9+8+2=20 and thus 0 is the fifth term and now we have 1, 9, 8, 2,0 The sixth term is given by 9+8+2+0 =19 and hence 9
Our sequence is now 1, 9, 8, 2, 0, 9,......
If continued in this fashion will this sequence ever have 3, 0, 4, 4 as part of the sequence after which it repeats itself?
Is there any way to say that the sequence will definitely repeat itself and if yes after how many terms? If not then why not?
Ajit
 
ajit said:
Repeating Integer Sequences:
Suppose the first four terms of a sequence are 1, 9, 8 and 2.
Now each susequent term is obtained by taking the last digit of the sum of the four previous terms.
So we get: 1+9+8+2=20 and thus 0 is the fifth term and now we have 1, 9, 8, 2,0 The sixth term is given by 9+8+2+0 =19 and hence 9
Our sequence is now 1, 9, 8, 2, 0, 9,......
If continued in this fashion will this sequence ever have 3, 0, 4, 4 as part of the sequence after which it repeats itself?
Is there any way to say that the sequence will definitely repeat itself and if yes after how many terms? If not then why not?
Ajit
Click to expand...
To answer your 1st question: yes.
1,9,8,2 being terms #1,2,3,4, then you'll get 3,0,4,4 as terms #1557,1558,1559,1560.
This will then repeat: 3117,3118,3119,3120; and so on.

To answer your other question: ask TKHunny :idea:
 
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