2 versions of Python code solving in O(n) time:

from collections import Counter

def pickingNumbers(a):
    c = Counter(a)
    return max( c[n]+c.get(n-1,0) for n in c )

version 2:

def pickingNumbers1(a):
    a = sorted(a)
    m=i=0
    while i<len(a):
        s=i
        while i<len(a) and abs(a[i]-a[s])<=1: i+=1
        m = i-s if i-s>m else m
    return m