Let's define a sevenish number is a number that is one of a power of 7, or a number that is the sum of unique power of 7s

sevenish_algorithm_problem_solution.py

'''
Let's define a sevenish number is a number that is one of a power of 7, or a number that is the sum of unique power of 7s

From the beginning the first few sevenish are:
1, 7, 8, 49, 50 and so on

You are to create an algorithm that finds the i'th sevenish number

'''

# i = 1, ret = 7^0 = 1 - base
# i = 2, ret = 7^1 = 7 - base
# i = 3, ret = 7^0 + 7^1 = 8 - base
# i = 4, ret = 7^2 = 49 - base
# i = 5, ret = 7^2 + 7^0 = 50
# i = 6, ret = 7^2 + 7^1 = 56
# i = 7, ret = 7^2 + 7^1 + 7^0 = 57 - base
# i = 8, ret = 7^3 = 343
# i = 9, ret = 7^3 + 7^0 = 344
# i = 10, ret = 7^3 + 7^1 = 350
# i = 11, ret = 7^3 + 7^1 + 7^0 = 351
# i = 12, ret = 7^3 + 7^2 = 392
# i = 13, ret = 7^3 + 7^2 + 7^0 =393
# i = 14, ret = 7^3 + 7^2 + 7^1 = 399
# i = 15, ret = 7^3 + 7^2 + 7^1 + 7^0 = 400 - base

def sevenish(n):
  last_power_index = 0
  add_index = 0
  mem = [1] * n

  for i in range(1, n):
    if add_index == last_power_index:
      add_index = 0
      mem[i] = mem[last_power_index] * 7
      last_power_index = i
    else:
      mem[i] = mem[last_power_index] + mem[add_index]
      add_index += 1

  return mem[-1]

# Test the solution
assert sevenish(1) == 1
assert sevenish(2) == 7
assert sevenish(7) == 57
assert sevenish(10) == 350
assert sevenish(11) == 351