A WELL-BEHAVED COUSIN OF THE HOFSTADTER SEQUENCE

被引：31
|
作者：
TANNY, SM
机构：
[1] Department of Mathematics, University of Toronto, Toronto
来源：
DISCRETE MATHEMATICS | 1992年 / 105卷 / 1-3期
关键词：
D O I：
10.1016/0012-365X(92)90145-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Very little is known about the Hofstadter sequence Q(n) defined by Q(1) = Q(2) = 1 and Q(n) = Q(n - Q(n - 1)) + Q(n - Q(n - 2)), n > 2. A seemingly close relative is the sequence T(n) given by T(n) = T(n - 1 - T(n - 1)) + T(n - 2 - T(n - 2)), n > 2 with T(0) = T(1) = T(2) = 1. In sharp contrast to the 'chaotic' behaviour of Q(n), T(n) behaves in a completely predictable fashion which is characterized precisely. In particular, T(n) is monotonic and hits every positive integer.
引用
收藏
页码：227 / 239
页数：13
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