keypad.js

var keypadPermutations = function (phone_number) {

	// Split phone number into array and parseInt each
	var digits = phone_number.split('').map(function(digit) {
		return parseInt(digit);
	});

	// Map letters to keys
	var KEYMAPS = [
		['0'], // 0,
		['1'], // 1,
		['a', 'b', 'c'], // 2
		['d', 'e', 'f'], // 3
		['g', 'h', 'i'], // 4
		['j', 'k', 'l'], // 5
		['m', 'n', 'o'], // 6
		['p', 'q', 'r', 's'], // 7
		['t', 'u', 'v'], // 8
		['w', 'x', 'y', 'z'] // 9
	];

	// Array to be populated with all possible sequences
	var solution = [];

	(function sequencer(progress, i) {
		if ((i === phone_number.length - 1)) {
			KEYMAPS[digits[i]].forEach(function(letter) {
				solution.push(progress + letter);
			});
		} else {
			KEYMAPS[digits[i]].forEach(function(letter) {
				sequencer(progress + letter, i+1);
			});
		}
	})('', 0); // Start with empty string and first digit

	return solution;
};

module.exports = keypadPermutations;

keypad.spec.js

var keypadPermutations = require('./keypad.js');

describe('keypadPermutations', function() {
	
	it('works for 2 digits', function() {
		var perms = keypadPermutations('23');
		var result = ['ad', 'ae', 'af', 'bd', 'be', 'bf', 'cd', 'ce', 'cf'];
		expect(perms).toEqual(result);
	});

	it('works for 3 digits', function() {
		var perms = keypadPermutations('234');		
		var result = ['adg', 'adh', 'adi', 'aeg', 'aeh', 'aei', 'afg', 'afh', 'afi', 'bdg', 'bdh', 'bdi', 'beg', 'beh', 'bei', 'bfg', 'bfh', 'bfi','cdg', 'cdh', 'cdi', 'ceg', 'ceh', 'cei', 'cfg', 'cfh', 'cfi'];
		expect(perms).toEqual(result);
	});

	it('works for number with 0', function() {
		var perms = keypadPermutations('023');		
		var result = ['0ad', '0ae', '0af', '0bd', '0be', '0bf', '0cd', '0ce', '0cf'];
		expect(perms).toEqual(result);
	});

	it('works for number with 1', function() {
		var perms = keypadPermutations('231');		
		var result = ['ad1', 'ae1', 'af1', 'bd1', 'be1', 'bf1', 'cd1', 'ce1', 'cf1'];
		expect(perms).toEqual(result);
	});

	it('works for 7 digits of 3 letters each', function() {
		var perms = keypadPermutations('2345682');
		expect(perms.length).toEqual(2187); // 3^7 = 2187
	});

	it('works for 7 digits of mixed number of letters each', function() {
		var perms = keypadPermutations('2345678');
		expect(perms.length).toEqual(2916); // 3^6 * 4 = 2916
	});
});