take-a-number-and-sum-its-digits-raised-to-the-consecutive-powersand-eureka.md

Take a Number And Sum Its Digits Raised To The Consecutive Powers And ....¡Eureka!! ^{6 Kyu}

^{LINK TO THE KATA - FUNDAMENTALS MATHEMATICS}

Description

The number $89$ is the first integer with more than one digit that fulfills the property partially introduced in the title of this kata. What's the use of saying "Eureka"? Because this sum gives the same number: $89=8^1+9^2$

The next number in having this property is $135$:

See this property again: $135=1^1+3^2+5^3$

Task

We need a function to collect these numbers, that may receive two integers $a,b$ that defines the range $[a,b]$ (inclusive) and outputs a list of the sorted numbers in the range that fulfills the property described above.

Examples

Let's see some cases (input -> output):

1, 10  --> [1, 2, 3, 4, 5, 6, 7, 8, 9]
1, 100 --> [1, 2, 3, 4, 5, 6, 7, 8, 9, 89]

If there are no numbers of this kind in the range $[a,b]$ the function should output an empty list.

90, 100 --> []

Enjoy it!!

Solution

const isEurekaNumber = num => {
  const sum = String(num)
    .split('')
    .reduce((acc, digit, index) => {
      return acc + Math.pow(Number(digit), index + 1)
    }, 0)

  return sum === num
}

const sumDigPow = (a, b) => {
  const eurekaNumbers = []

  for (let i = a; i <= b; i++) {
    if (isEurekaNumber(i)) eurekaNumbers.push(i)
  }

  return eurekaNumbers
}