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EXAMPLE
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The sequence of terms together with their corresponding compositions begins:
0: () 593: (3,2,4,1) 16937: (5,4,2,3,1)
1: (1) 600: (3,2,1,4) 16940: (5,4,2,1,3)
5: (2,1) 610: (3,1,4,2) 16946: (5,4,1,3,2)
6: (1,2) 616: (3,1,2,4) 16948: (5,4,1,2,3)
37: (3,2,1) 649: (2,4,3,1) 16965: (5,3,4,2,1)
38: (3,1,2) 652: (2,4,1,3) 16966: (5,3,4,1,2)
41: (2,3,1) 657: (2,3,4,1) 16977: (5,3,2,4,1)
44: (2,1,3) 664: (2,3,1,4) 16984: (5,3,2,1,4)
50: (1,3,2) 708: (2,1,4,3) 16994: (5,3,1,4,2)
52: (1,2,3) 712: (2,1,3,4) 17000: (5,3,1,2,4)
549: (4,3,2,1) 786: (1,4,3,2) 17033: (5,2,4,3,1)
550: (4,3,1,2) 788: (1,4,2,3) 17036: (5,2,4,1,3)
553: (4,2,3,1) 802: (1,3,4,2) 17041: (5,2,3,4,1)
556: (4,2,1,3) 808: (1,3,2,4) 17048: (5,2,3,1,4)
562: (4,1,3,2) 836: (1,2,4,3) 17092: (5,2,1,4,3)
564: (4,1,2,3) 840: (1,2,3,4) 17096: (5,2,1,3,4)
581: (3,4,2,1) 16933: (5,4,3,2,1) 17170: (5,1,4,3,2)
582: (3,4,1,2) 16934: (5,4,3,1,2) 17172: (5,1,4,2,3)
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