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Repeated Digits (Posted on 2014-01-14) Difficulty: 2 of 5
Define the sequence A(n) as: A(1) = 1, A(2) =13, A(3) = 131, A(4) = 1313,...
  1. Determine the minimum value of n such that A(n) is divisible by 29.
  2. What is the general form of n such that A(n) is divisible by 29?

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 2 of 2 |

10   A="1":N=1
20   while Ct<40
30      if val(A) @ 29=0 then print N,N-Prev,N @ 28:inc Ct:Prev=N
40      if right(A,1)="1" then A=A+"3":else A=A+"1"
50      inc N
60   wend

finds

valid   diff   mod 28
  n     from
        prev
 9       9       9
 28      19      0
 37      9       9
 56      19      0
 65      9       9
 84      19      0
 93      9       9
 112     19      0
 121     9       9
 140     19      0
 149     9       9
 168     19      0
 177     9       9
 196     19      0
 205     9       9
 224     19      0
 233     9       9
 252     19      0
 261     9       9
 280     19      0
 289     9       9
 308     19      0
 317     9       9
 336     19      0
 345     9       9
 364     19      0
 373     9       9
 392     19      0
 401     9       9
 420     19      0
 429     9       9
 448     19      0
 457     9       9
 476     19      0
 485     9       9
 504     19      0
 513     9       9
 532     19      0
 541     9       9
 560     19      0


 
The valid n are congruent to either 9 or 0 mod 28.

The printing of N @ 28 (i.e., N mod 28) was added of course after seeing the difference column alternate 9 and 19.


 


  Posted by Charlie on 2014-01-14 11:55:29
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