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 Repeated Digits (Posted on 2014-01-14)
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 No Rating

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 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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