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EXAMPLE
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The terms together with their binary expansions and binary indices begin:
2: 10 ~ {2}
3: 11 ~ {1,2}
7: 111 ~ {1,2,3}
23: 10111 ~ {1,2,3,5}
31: 11111 ~ {1,2,3,4,5}
127: 1111111 ~ {1,2,3,4,5,6,7}
311: 100110111 ~ {1,2,3,5,6,9}
383: 101111111 ~ {1,2,3,4,5,6,7,9}
991: 1111011111 ~ {1,2,3,4,5,7,8,9,10}
2039: 11111110111 ~ {1,2,3,5,6,7,8,9,10,11}
3583: 110111111111 ~ {1,2,3,4,5,6,7,8,9,11,12}
6143: 1011111111111 ~ {1,2,3,4,5,6,7,8,9,10,11,13}
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