hippyish.py

def happyish_sequence(numbers):
    # Take the last number from the list and convert to a string
    number = numbers[-1]
    s_number = str(number)

    # If it's only one digit, then square it
    if len(s_number) == 1:
        output = number**2
    # Otherwise find the difference
    else:
        output = abs((int(s_number[0])**2) - (int(s_number[1])**2))
    # Add to the list
    numbers.append(output)
    # If the last two numbers are the same or we have more than 10 then return
    if output == numbers[-2] or len(numbers) > 10:
        return numbers
    # Otherwise continue the sequence
    else:
        return happyish_sequence(numbers)


count_happyish = 0

for i in range(1,100):
    list_nums = happyish_sequence([i])
    if list_nums[-1] == 0:
        print(list_nums)
        count_happyish += 1
# For extension - show the other patterns ending in duplicate numbers
#    elif list_nums[-1] == list_nums[-2]:
#        print("NOT -- ",list_nums)

print(count_happyish)

Example output:

[7, 49, 65, 11, 0, 0]
[11, 0, 0]
[22, 0, 0]
[29, 77, 0, 0]
[33, 0, 0]
[34, 7, 49, 65, 11, 0, 0]
[38, 55, 0, 0]
[43, 7, 49, 65, 11, 0, 0]
[44, 0, 0]
[47, 33, 0, 0]
[49, 65, 11, 0, 0]
[55, 0, 0]
[56, 11, 0, 0]
[59, 56, 11, 0, 0]
[65, 11, 0, 0]
[66, 0, 0]
[70, 49, 65, 11, 0, 0]
[74, 33, 0, 0]
[77, 0, 0]
[83, 55, 0, 0]
[88, 0, 0]
[92, 77, 0, 0]
[94, 65, 11, 0, 0]
[95, 56, 11, 0, 0]
[99, 0, 0]
25