# input pattern we are looking for and helper information about it
pattern = "652601"
patternInt = int( pattern)
patternDigitsMagnitude = 10**len( str( pattern))

# start from the [ 3  7  1 [0](1) 0 ] as initial position
# to avoid checking an additional condition inside the loop
recipes = [ 3, 7, 1, 0, 1, 0]
elf1CNodeIdx = 4
elf2CNodeIdx = 3

currentRunningPattern = 371010 % patternDigitsMagnitude
while True:
    lenRecipes = len( recipes)
    #make recipes
    elf1CNodeVal = recipes[elf1CNodeIdx]
    elf2CNodeVal = recipes[elf2CNodeIdx]
    newRecipesSum = elf1CNodeVal + elf2CNodeVal
    if newRecipesSum > 9: # if the sum is ge 10 adds an additional second node
        recipes.append( 1) # node we are adding is always 1
        newRecipesSum -= 10
        #pattern scan
        currentRunningPattern *= 10
        currentRunningPattern += 1 # node we are adding is always 1
        currentRunningPattern %= patternDigitsMagnitude
        if currentRunningPattern == patternInt:
            print( "The pattern occurs at: ", len( recipes) - len( pattern))
            break
    recipes.append( newRecipesSum) # always add at least one node
    #pattern scan
    currentRunningPattern *= 10
    currentRunningPattern += newRecipesSum
    currentRunningPattern %= patternDigitsMagnitude
    if currentRunningPattern == patternInt:
        print( "Pattern occurs at position: ", len( recipes) - len( str( pattern)))
        break
    #advance elves
    elf1CNodeIdx = (elf1CNodeIdx + (elf1CNodeVal + 1)) % len( recipes)
    elf2CNodeIdx = (elf2CNodeIdx + (elf2CNodeVal + 1)) % len( recipes)