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#!/usr/bin/env node
// Week 147 Task 2
// Pentagon Numbers
// Write a sript to find the first pair of Pentagon Numbers
// whose sum and difference are also a Pentagon Number.
// Answer: First pair is 1560090 and 7042750
var pentagonal_numbers = [1]
var pair_found = false
var number = 2
while (!pair_found) {
let next_pn = pentagonal_number(number)
for (let i = 0; i < pentagonal_numbers.length; i++) {
if ((is_pentagonal_number(next_pn - pentagonal_numbers[i])) &&
(is_pentagonal_number(next_pn + pentagonal_numbers[i]))) {
console.log('First pair are ' + pentagonal_numbers[i] + ' and ' + next_pn)
pair_found = true
break
}
}
pentagonal_numbers.push(next_pn)
number++
}
function pentagonal_number (number) {
return ( ( 3 * ( number * number ) ) - number ) / 2
}
function is_pentagonal_number (number) {
let remainder = ( Math.sqrt( 24 * number + 1 ) + 1 ) % 6;
if ( remainder > 0 ) {
return false
}
else {
return true
}
}
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