Pattern Recognition - 2

Can you find 10^th, 21^st, 50^th, 101^st and 1000^th element in this pattern?

 

0,2,1,4,1,6,2,8,…………


Answer

It is combination of two number series.

0,2,1,4,1,6,2,8,…………

1. Fibonacci series - http://www.mathsisfun.com/numbers/fibonacci-sequence.html

          0,_,1,_,1,_,2……

   2. Even number series
         _,2,_,4,_,6,_,8……
 
All the even count elements will be from even number series and odd count elements will be from Fibonacci series.

10^th element will be 10/2 = 5^th even number – 10
21^st element will be (21+1)/2 =11^th fibonacci number -55
50^th element will be 50/2 =25^th even number -50
101^st element will be 101+1/2 =51^st Fibonacci number – 12586269025
1000^th element will be 1000/2=500^th even number -1000

To find nth fibonacci number

private long FindFibonacciNumber(int n)

        {

            long i=0,k = 0;

            long j = 1;

            if (n == 1)

                return 0;

            if (n == 2)

                return 1;

            for (long count= 3; count <= n; count++)

            {

                k = i + j;

                i = j;

                j = k;       

            }

            return k;

        }