Square root sequences

sqrtSeq.py

#!/usr/bin/python
""" Ascending/descending sequence spotter, looking
    for sequences in the first decimal places of
    square roots.

  https://twitter.com/standupmaths/status/518081757019906048
"""
import decimal
import json
import signal

stateFile = 'sqrtSeq.json'
savePeriod = 3600

# Restore saved state, so we can continue from where we left off
try:
  state = json.load(file(stateFile, 'r'))
  curLen = state['length']
  i = state['current']
  print "Restored state: ", i, curLen
except:
  curLen = 5
  i=1
  print "Initial state: ", i, curLen

# Ensure we have enough precision to resume
decimal.getcontext().prec = curLen*2

# Save state on ctrl-c or every hour, just to be safe
def saveState(sig, frame):
  print "Saving state: ", i, curLen
  state = { 'current': i, 'length': curLen}
  json.dump(state, file(stateFile, 'w'))
  if sig == signal.SIGINT:
    exit(1)

signal.signal(signal.SIGINT, saveState)
if savePeriod > 0:
  signal.signal(signal.SIGALRM, saveState)
  signal.setitimer(signal.ITIMER_REAL, savePeriod, savePeriod)


def ascRun(a):
  """ Measure the length of the ascending sequence in a """
  for i in range(len(a)-1):
    if a[i] > a[i+1]:
      return i+1
  return len(a)

def dscRun(a):
  """ Measure the length of the descending sequence in a """
  for i in range(len(a)-1):
    if a[i] < a[i+1]:
      return i+1
  return len(a)


while True:
  root = str(decimal.Decimal(i).sqrt())
  if '.' in root:
    fract = root.split('.')[1]
    if ascRun(fract) >= curLen:
      print "ASC", i, ascRun(fract), root
      curLen = ascRun(fract)
      decimal.getcontext().prec = curLen*2
    elif dscRun(fract) >= curLen:
      print "DSC", i, dscRun(fract), root
      curLen = dscRun(fract)
      decimal.getcontext().prec = curLen*2
  i += 1