| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | --- | 
					
						
							|  |  |  | id: 5900f44e1000cf542c50ff60 | 
					
						
							|  |  |  | title: 'Problem 225: Tribonacci non-divisors' | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | challengeType: 5 | 
					
						
							| 
									
										
										
										
											2019-08-05 09:17:33 -07:00
										 |  |  | forumTopicId: 301868 | 
					
						
							| 
									
										
										
										
											2021-01-13 03:31:00 +01:00
										 |  |  | dashedName: problem-225-tribonacci-non-divisors | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | --- | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | # --description--
 | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | The sequence 1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201 ... | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | is defined by T1 = T2 = T3 = 1 and Tn = Tn-1 + Tn-2 + Tn-3. | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							|  |  |  | It can be shown that 27 does not divide any terms of this sequence.In fact, 27 is the first odd number with this property. | 
					
						
							|  |  |  | 
 | 
					
						
							|  |  |  | Find the 124th odd number that does not divide any terms of the above sequence. | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | # --hints--
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | `euler225()` should return 2009. | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | ```js | 
					
						
							|  |  |  | assert.strictEqual(euler225(), 2009); | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | ``` | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | # --seed--
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | ## --seed-contents--
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							|  |  |  | ```js | 
					
						
							|  |  |  | function euler225() { | 
					
						
							| 
									
										
										
										
											2020-09-15 09:57:40 -07:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  |   return true; | 
					
						
							|  |  |  | } | 
					
						
							|  |  |  | 
 | 
					
						
							|  |  |  | euler225(); | 
					
						
							|  |  |  | ``` | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | # --solutions--
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							|  |  |  | ```js | 
					
						
							|  |  |  | // solution required | 
					
						
							|  |  |  | ``` |