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It ain't Fibonacci (Posted on 2005-02-22) Difficulty: 3 of 5
Find the pattern and state the next few numbers.

0 0 1 3 2 6 5 13 12 14 11 27 24 ...

Does this sequence ever revert back to a single digit number? If so, when?

See The Solution Submitted by Erik O.    
Rating: 4.0000 (2 votes)

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Solution Partial Solution | Comment 7 of 10 |

I took Jer's observation and extended it to more digits and more prime numbers.

The first 81:

0
0
1
3
2
6
5
13
12
14

11
27
24
56
49
55
54
118
117
245

240
250
235
491
488
492
461
463
454
454

450
1474
1473
1491
1428
1440
1437
3485
3358
3392

3387
7483
7474
15666
15649
15655
15400
31784
31781
31789

31786
31852
31819
64587
64586
64606
64597
64727
64727
130263

130256
261328
260305
260315
260314
260350
260333
522477
522412
522670

522659
1046947
1046944
2095520
2093473
2093479
2093350
2093374
2093341
4190493

4190488

I still don't know if it will ever revert back to a single digit number. I know the first 10000 terms (besides the first 7) all have more than one digit.  I suspect that it will never again have a one-digit term, but I can't prove it.

If there are two consecutive primes, a and b, and b > 2a, the terms between 2a and b have a chance, if they don't hit any other primes.  There are no such primes in the first thousand primes.  I have not checked further.


  Posted by Dustin on 2005-02-28 20:30:02
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