#Returns all partitions of n.
#
#See:  Jerome Kelleher and Barry O'Sullivan, Generating All Partitions: A Comparison Of Two Encodings, arXiv:0909.2331 [cs.DS], 2009-2014.
def accelAsc(n):
    a = [0 for i in range(n + 1)] 
    k = 1 
    y = n - 1
    while k != 0:
        x = a[k - 1] + 1
        k -= 1
        while 2*x <= y:
            a[k] = x
            y -= x
            k += 1
        l = k + 1
        while x <= y:
            a[k] = x
            a[l] = y
            yield a[:k + 2]
            x += 1
            y -= 1
        a[k] = x + y
        y = x + y - 1
        yield a[:k + 1]

def isPrime(n):
    n=abs(int(n))
    if n<2:
        return False
    if n==2:
        return True
    if not n&1:
        return False
    for x in range(3,int(n**0.5)+1, 2):
        if n%x==0:
            return False
    return True

seq = []
ct = 0
max = 0
for n in range(21):
  prtns = list(accelAsc(n))
  for i in range(max, n):
    ct = 0
    for prtn in prtns:
      pct = 0
      for k in prtn:
        if isPrime(k):
          pct += 1
      if pct == i:
        ct += 1
    if ct == i:
      max = ct
      seq.append(n)
    if ct == 0:
      break

print(seq)