
EXAMPLE

The starting value x = 549 leads to 1503 > 6813 > 15444 > 7722 which is element of the cycle [3861, 12492, 6246, 3123, 6444, 3222, 1611, 7722] of length 8, with representative = smallest member a(1) = 1611.
The starting value x = 9203 leads to the cycle (18523, 103844, 51922, 25961, 122482, 61241, 125452, 62726, 31363, 94694, 47347, 124790, 62395, 158927, 1146448, 573224, 286612, 143306, 71653, 148184, 74092, 37046, 18523) of length = 22 with (smallest) representative a(2) = 18523.
The starting value x = 36037 leads to 112367 > 875578 > 437789 > 1425532 > 712766 > 356383 > 1221716, element of the cycle (610858, 305429, 1259749, 11235170, 5617585, 14383136, 7191568, 3595784, 1797892, 898946, 449473, 1423916, 711958, 355979, 1353532, 676766, 338383, 1221716) of length 18, with (smallest) representative a(4) = 305429.
The starting value x = 84807 leads to 173547 > ... > 5637789 > 15515442 which is part of the cycle (7772121, 15544332, 7772166, 3886083, 12772413, 90204624, 45102312, 22551156, 11275578, 5637789, 15515442, 7757721, 15535242, 7767621, 15544242) of length 15 and (smallest) representative 3886083.
The starting value x = 104481 leads to 948591 > 1947132 part of the cycle (973566, 486783, 1374426, 687213, 1563534, 781767, 1659528, 829764, 414882, 207441, 951651, 1917162, 958581, 1947132) of length 14 with (smallest) representative a(3) = 207441.
We actually don't know that this is a(3) until we have checked that no smaller starting value will produce a smaller term. Similarly, we know the index of a(4) only after checking all (odd) starting values less than a(4).
