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A successive method of deriving the necklaces of higher lengths from the lower ones when the absolute  difference of two adjacent beads  (DBs) belongs to a specified set of numbers is developed. Some of them can be obtained in sequence; while others are obtained from even length to next even length, or odd length to next odd length. There are many possible necklaces for the same length. The technique is extended to DBs with different sets of numbers which include 1. Gluing method is developed which gives the higher length necklaces from lower ones by interconnecting two necklaces.

Higher Length Necklaces from Lower Ones When the Absolute Value of the Difference of Two Adjacent Beads Belongs to a Set of Integers