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Next year (Posted on 2013-09-03) Difficulty: 2 of 5
Consider two series a: 1,2,3,5 and b: 4,9,14,19,24.. defined as follows:

a(n) is the smallest positive integer not appearing in the set

( a(1),a(2),a(3),a(n-1),b(1),b(2),b(3),b(n-1)).

b(n)=5n-1

Evaluate a(2014) .
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No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (2 votes)

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Solution General solution (spoiler) Comment 1 of 1
It looks like series a is all positive integers which are not of the form 5n - 1.

a(n) = 5 + a(n-4),
so
a(2014) = a(503*4 + 2) = 5*503 + a(2) = 2517.

In general, a(n) = 5*[n/4] + (n mod 4)

Hope I haven't made a mistake

  Posted by Steve Herman on 2013-09-03 11:45:20
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