Dropping patterns of the 3x+1 (Collatz) iteration.
1, 110, 1101, 1110, 110110, 111010, 111100, 1101101, 1101110, 1110101, 1110110, 1111001, 1111010, 1111100, 110110110, 110111010, 110111100, 111010110, 111011010, 111011100, 111100110, 111101010, 111101100, 111110010, 111110100, 111111000, 11011011010
1
There are only a finite number of dropping patterns for each iteration length. For length 4, the patterns are 1101 and 1110, which are formed by an infinite number of numbers, but the smallest two are 11 and 23.
T. D. Noe, Plot of 56 terms
T. D. Noe, Table of 56 terms
(Mma) toBinary[lst_List] := FromDigits[(Sign[Rest[lst] - Most[lst]] + 1)/2]; Collatz[n_] := Most[NestWhileList[If[EvenQ[#], #/2, (3 # + 1)/2] &, n, # >= n &]]; Join[{1}, Sort[toBinary /@ Collatz /@ {3, 11, 23, 7, 15, 59, 39, 79, 95, 123, 175, 199, 219, 287, 347, 367, 423, 507, 575, 583, 735, 815, 923, 975, 999}]]
nonn,tabf,nice
T. D. Noe, Sep 23 2014