Armstrong Numbers

we start the problem series on PMC (Python Members Club) with Armstrong Numbers.

definition

an armstrong number is a number such that the sum of the digits in the number raised to the number of digits equals the number itself

breaking down

sum of the digits in the number

let us take number abc, sum is

a + b + c

raised to the number of digits

num of digits in abc is 3

a^3 + b^3 + c^3

equals the number itself

a^3 + b^3 + c^3 == abc

examples

1 – 123, number of digits: 3, hence risen to power 3

1^3 + 2^3 + 3^3 -> 36, not equals 123

2 – 153 , number of digits: 3, hence risen to power 3

1^3 + 5^3 + 3^3 ->1 + 125 + 27 -> 153, sum same as number

3 – 8208, number of digits, hence risen to power 4

8^4 + 2^4 + 0^4 + 8^4 ->4096 + 16 + 0 + 4096-> 8208, sum same as number

our code

for i in range(1000000):
num = str(i)
sumcube = 0
for n in num:
sumcube += (int(n) ** len(num))
if i == sumcube:
print(i, 'is an armstrong number')

the logic

for i in … spits out a number each time for us to deal with

num = str(i) transform the integer into string …

… which allows us a neat python trick: iterating over a string. that way we instantly get the 3 1 9 of 319. the conventional approach would have been to divide by 100 10 and 1 to get 3 1 9

nothing spooky, out of reach eh …

anything? drop a word below ^^

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• appinv

Lives in Mauritius, cruising python waters for now.