The Comma Sequence: A Simple Sequence With Bizarre Properties
arxiv(2024)
摘要
The “comma sequence” starts with 1 and is defined by the property that if k
and k' are consecutive terms, the two-digit number formed from the last digit
of k and the first digit of k' is equal to the difference k'-k. If there is
more than one such k', choose the smallest, but if there is no such k' the
sequence terminates. The sequence begins 1, 12, 35, 94, 135, ... and,
surprisingly, ends at term 2137453, which is 99999945. The paper analyzes the
sequence and its generalizations to other starting values and other bases. A
slight change in the rules allows infinitely long comma sequences to exist.
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