The nth digit in a sequence program

Overview

Given an integer n find the nth digit in the infinite sequence {1, 2, 3, 4 ….. infinity}

Example

Input: 14
Output: 1

The 14th digit of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 … is a 1, which is part of the number 12.

Example 2

Input: 17
Output: 3

The 17th digit of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 … is a 3, which is part of the number 13.

Program

Here is the program for the same.

package main

import "fmt"

func findNthDigit(n int) int {

	numDigits := 1
	tenIncrement := 1

	start := 1
	counter := 9 * tenIncrement * numDigits

	for n > counter {
		n = n - counter
		tenIncrement = tenIncrement * 10
		numDigits++
		start = start * 10
		counter = 9 * tenIncrement * numDigits
	}

	return findNthDigitUtil(start, numDigits, n)

}

func findNthDigitUtil(start, numDigits, n int) int {
	position := n % numDigits
	digitWhichHasN := 0
	if position == 0 {
		digitWhichHasN = start - 1 + n/numDigits
		return digitWhichHasN % 10
	} else {
		digitWhichHasN = start + n/numDigits
		positionFromBehind := numDigits - position
		answer := 0
		for positionFromBehind >= 0 {
			answer = digitWhichHasN % 10
			digitWhichHasN = digitWhichHasN / 10
			positionFromBehind--
		}
		return answer
	}

	return 0

}

func main() {
	output := findNthDigit(14)
	fmt.Println(output)

	output = findNthDigit(17)
	fmt.Println(output)
}

Output

1
3