# Python program for OEIS A051652
# Michael S. Branicky, Feb 27 2021

# dedicated to Lydia on her half birthday

from sympy import nextprime, prevprime
from time import time

time0 = time()
PRINTEVERY = 10**9
printat = PRINTEVERY

A051652 = {0:2, 2:0}
p, q, r = 0, 2, 3

def record(idx, m):
  A051652[idx] = m
  print("FOUND", idx, m, time()-time0)
  print("   ", A051652)
  alst = []
  with open('b051652.txt', 'w') as f:
    for i in range(max(A051652)+1):
      if i in A051652:
        ai = A051652[i]
      else:
        ai = '?'
      alst.append(ai)
      f.write(f"{i} {ai}\n")
  print("   ", alst)

while True:
  gap1 = q - p
  quot1, rem1 = divmod(gap1, 2)
  for cq in range(quot1+1):
    if cq not in A051652:
      m = p + cq
      idx = cq
      record(idx, m)
  gap2 = min(q - p, r - q)
  if gap2 not in A051652:
    m = q
    idx = gap2
    record(idx, m)
    
  if p >= printat:
    print("...", p, time()-time0)
    printat += PRINTEVERY
  p, q, r = q, r, nextprime(r)