Question

How to find the first integer equal to the sum of its digits raised to some power in JavaScript

Answer 1

// compute sum of digits
function digitSum(n) {
    let s = 0;

    while (n > 0) {
        s += n % 10;
        n = Math.floor(n / 10);
    }

    return s;
}

function main() {
    for (let n = 2; ; n++) {
        const s = digitSum(n);

        // Try powers k = 2..10 (enough for reasonable ranges)
        let p = s * s;
        for (let k = 2; k <= 10; k++) {
            if (p === n) {
                console.log(`Found: ${n} = (${s})^${k}`);
                return;
            }
            p *= s; // next power
        }
    }
}

main();



/*
run:

Found: 81 = (9)^2

*/

 

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