Consider the function F(N) = 2^N + 1 where N is a positive integer less than 31. Given such a list of 5 integers, find the one that was swapped in and is therefore not part of the original 5 contiguous integers.

OddOneOut.scala

//http://codegolf.stackexchange.com/questions/94679/find-the-odd-one-out-in-a-sequence
import math._

object OddOneOut{
	case class Test(val l: Seq[Double],val expected: Double){
		def apply( _l: Seq[Double], _e: Double ) = new Test( _l, _e )
	}
	
	def log2(x: Double) = math.log(x)/math.log(2)

	//y = 1 + 2^n
	//n = log2(y-1)
	def n(y: Double) = log2(y-1)
	//if N is valid then it does not have a decimal poDouble
	def validN(y: Double): Boolean = ( n(y)%1 == 0 )
	//
	def validSequence(seq: Seq[Double]): Boolean = seq.sliding(2).map(a => a(0)+1 == a(1)).count(identity) > 0

	def main(args: Array[String]) {
		Seq(
			Test(Seq(5,9,17,33,829), 829 ),
			Test(Seq(9,5,17,829,33), 829 ),
			Test(Seq(33, 17, 5, 7, 65),7),
			Test(Seq(5,9,177,33,65),177),
			Test(Seq(65,129,259,513,1025), 259),
			Test(Seq(129,259,513,1025,65), 259),
			Test(Seq(63,129,257,513,1025), 63),
			Test(Seq(65,129,257,513,4097), 4097),
			Test(Seq(5, 9, 2, 17, 33), 2),
			Test(Seq(9,67108865,134217729,1,268435457), 1)
		).map{
			case Test(l, e) => {
				val odd = l.filterNot(validN)
				assert( 
					if(odd.isEmpty) validSequence( l.map{n(_).toDouble} ) else odd == Seq(e)
				, Test(l, e) )	
			}
		}
	}
}