Ascher Databook Notes:
  1. The twisted ends of the main cord and pendant 1 are linked together: Pendant 1 is a long cord containing flags and knots. The flags are constructed as follows:
    1. 4 strands of cord colored BG of about 4.0 cm. in length are passed through the pendant cord;
    2. They are then knotted around the cord. Knots and flags are spaced along the pendant at the following positions:

      4L (4.0); F (4.5); 7L (6.0); F (7.5); 1s(10.0); 2L (11.5); F (12.5); 1s (13.5);
      4L (15.5); F (17.0); 1s (l9.0); 5L (20.5); F (21.0); 2s (22.0); F (23.0); 1s (23.5);
      5L (26.0); F (27.0); 1s(28.0); 8L (29.5); F (30.0); 2s(31.0); 7L (34.0); F (35.5);
      1s(37.5); 5L (39.5); F (40.5); 1s(41.5); 3L (43.0); F (44.5); 1s (46.0); F (47.5);
      1s(49.0); 6L (51.0); F (52.0); 1s(53.0); 2L (54.5); F (55.5); 1s(57.5); 1E (59.5);
      F (6 1.0); 8L (63.5); end b (121.5).

      These can be interpreted as 16 numbers set off from each other by the interspersed flags. The consecutive values are 4, 7, 12, 14, 15, 20, 15, 18, 27, 15, 13, 10, 16, 12, 11, 8.

  2. When the values on pendant 1 are associated such that the first and last are paired, the second and next to last are paired, etc., some regularities can be seen.
    1. \[X_{1}+X_{16}=12\]
      \[X_{2}+X_{15}=18\]
      \[X_{3}+X_{14}=24\]
      \[X_{4}+X_{13}=30\]
      Thus for all:
      \[X_{i}+X_{17-i}=6(i+1)\;\;for\;i\;=\;(2,3,4)\]
    2. Patterns of divisibility are the same for the first and last four as compared to the second and third four.

      Then for all Y=4, for all i=1 and for all Y=5 for all i=5

      Xi and X17-i are both divisible by Y
      Xi+l and X17-(i+l) are relatively prime
      Xi+2 and X17-(i+2) are equal, both are divisible by Y and Xi+2/Y = 3
      Xi+3 and X17-(i+3) are both divisible by Y-2