| 词条 | Katydid sequence |
| 释义 |
The Katydid sequence is a sequence of numbers first defined in Clifford A. Pickover's book Wonders of Numbers (2001). DescriptionIt is the smallest sequence of integers that can be reached from 1 by a sequence of the two operations n ↦ 2n + 2 and 7n + 7 (in any order).[1] For instance, applying the first operation to 1 produces the number 4, and applying the second operation to 4 produces the number 35, both of which are in the sequence. The first 10 elements of the sequence are:[2] 1, 4, 10, 14, 22, 30, 35, 46, 62, 72. RepetitionsPickover asked whether there exist numbers that can be reached by more than one sequence of operations.[1] The answer is yes. For instance, 1814526 can be reached by the two sequences 1 – 4 – 10 – 22 – 46 – 329 – 660 – 4627 – 9256 – 18514 – 37030 – 259217 – 1814526 and 1 – 14 – 30 – 62 – 441 – 884 – 1770 – 3542 – 7086 – 14174 – 28350 – 56702 – 113406 – 226814 – 453630 – 907262 – 1814526 References1. ^1 {{cite book|title=Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning|first=Clifford A.|last=Pickover|publisher=Oxford University Press|year=2001|isbn=9780195348002|page=330|url=https://books.google.com/books?id=52N0JJBspM0C&pg=PA330}} {{Numtheory-stub}}2. ^{{Cite OEIS|A060031|name=Katydid sequence: closed under n -> 2n + 2 and 7n + 7}} 1 : Integer sequences |
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