JavaScript Program to Print Nth Non Fibonacci Number

JavaScript program to print the nth non-Fibonacci number. Non-Fibonacci numbers are integers that are not part of the Fibonacci sequence.

Below are the approaches to print the Nth non-Fibonacci number:

Using a Loop

We are using a while loop to find the nth non-Fibonacci number. we iterate through Fibonacci numbers and we skip them in the count until we reach the nth non-Fibonacci number. We do this by maintaining three variables (prev1, prev2, and cur) to track the current Fibonacci numbers. We decrement N by the difference between the current Fibonacci number and the previous Fibonacci number minus 1 to skip over Fibonacci numbers. After the loop, we adjust N back to get the correct non-Fibonacci number.

Example: To demonstrate printing the nth Non Fibonacci number using a loop.

function findNthNonFibonacci(N) {
    let prev1 = 2, prev2 = 1, cur = 3;

    while (N > 0) {
        let next = prev2 + prev1;
        prev2 = prev1;
        prev1 = next;
        cur = prev2 + prev1;

        N = N - (cur - prev1 - 1);
    }

    N = N + (cur - prev1 - 1);

    return prev1 + N;
}

const n = 9;
let nthNonFib = findNthNonFibonacci(n);
console.log(nthNonFib);

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Using Recursion

This recursive method finds the nth non-Fibonacci number by continuously calculating Fibonacci numbers. It keeps track of the count of non-Fibonacci numbers between consecutive Fibonacci numbers to determine the position of the nth non-Fibonacci number accurately. The function adjusts its search range based on this count and it stops when it finds the nth non-Fibonacci number.

Example: To demonstrate printing the nth Non Fibonacci number using recursion.

function findNthNonFibonacci(N, prev1 = 2, prev2 = 1, cur = 3) {
    if (N === 0) {
        return prev1 - 1; // Found the nth non-Fibonacci number
    }

    let next = prev2 + prev1;
    prev2 = prev1;
    prev1 = next;
    cur = prev2 + prev1;

    let nonFibCount = cur - prev1 - 1;

    if (N <= nonFibCount) {
        return prev1 + N;
    } else {
        return findNthNonFibonacci(N - nonFibCount, prev1, prev2, cur);
    }
}

const n = 5;
const nthNonFib = findNthNonFibonacci(n);
console.log(nthNonFib);

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