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								id: 5900f4c11000cf542c50ffd3
							 
						 
					
						
							
								
									
										
										
										
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								title: 'Problem 341: Golomb''s self-describing sequence'
							 
						 
					
						
							
								
									
										
										
										
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								challengeType: 5
							 
						 
					
						
							
								
									
										
										
										
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								forumTopicId: 302000
							 
						 
					
						
							
								
									
										
										
										
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								dashedName: problem-341-golombs-self-describing-sequence
							 
						 
					
						
							
								
									
										
										
										
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								# --description--
  
						 
					
						
							
								
									
										
										
										
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								The Golomb's self-describing sequence {G(n)} is the only nondecreasing sequence of natural numbers such that n appears exactly G(n) times in the sequence. The values of G(n) for the first few n are
							 
						 
					
						
							
								
									
										
										
										
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								n123456789101112131415…G(n)122334445556666…
							 
						 
					
						
							
								
									
										
										
										
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								You are given that G(103) = 86, G(106) = 6137. You are also given that ΣG(n3) = 153506976 for 1 ≤ n <  103.
							 
						 
					
						
							
								
									
										
										
										
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								Find ΣG(n3) for 1 ≤ n <  106.
							 
						 
					
						
							
								
									
										
										
										
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								# --hints--
  
						 
					
						
							
								
									
										
										
										
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								`euler341()`  should return 56098610614277016. 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
									
										
										
										
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								assert.strictEqual(euler341(), 56098610614277016);
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --seed--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								## --seed-contents--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								function euler341() {
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								euler341();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --solutions--
  
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```