longest_seq.py

def find_longest_sequence(arr):

    start = 0
    seq_result = []
    
    def sum_array(arr):
        _sum = 0
        for x in arr:
            _sum += x
        return _sum

    if len(arr) == 1:
        return arr
    
    for x in xrange(0,len(arr)):
        _max = arr[x]
        _min = arr[x]
        seq = []        
        
        for y in xrange(x,len(arr)):
            seq.append(arr[y])

            _min = min(arr[y],_min)
            _max = max(arr[y],_max)

            if len(seq) == 1:
                continue

            result_sum = sum_array(seq)
        
            if result_sum + (_min-1)*_min/2 == _max*(_max+1)/2:
                if not seq_result or len(seq_result) < len(seq):
                    seq_result = seq[:]
        
    return seq_result

a = [20,19,12,10,7,4,1,6,5,3,2,90,49]

print find_longest_sequence(a)