整数序列杂志 Vol. 18(2015)第15条第7款

The Yellowstone Permutation


戴维·L·阿普盖特
美国电话电报公司
AT&T方式
贝德明斯特,新泽西州07921
美国

汉斯哈弗曼
11 Sykes Ave.
Weston,在M9N 1C8上
加拿大

罗伯特·G·塞尔科
16214马德伍德街
柏树,德克萨斯州77429
美国

弗拉迪米尔谢维列夫
数学系
本古里安大学
啤酒什瓦84105
以色列

斯隆
OEIS基金会
11南阿德莱德大道。
高地公园,NJ 08904
美国

莱因哈德祖姆勒
Isabellastrasse 13
慕尼黑D80798
德国

摘要

Define a sequence of positive integers by the rule that a(n) = n for 1 ≤ n ≤ 3, and for n ≥ 4, a(n) is the smallest number not already in the sequence which has a common factor with a(n - 2) but is relatively prime to a(n - 1). We show that this is a permutation of the positive integers. The remarkable graph of this sequence consists of runs of alternating even and odd numbers, interrupted by small downward spikes followed by large upward spikes, suggesting the eruption of geysers in Yellowstone National Park. On a larger scale the points appear to lie on infinitely many distinct curves. There are several unanswered questions concerning the locations of these spikes and the equations for these curves.


完整版:PDFDVI聚苯乙烯乳胶    


(与序列有关)A000 6368 A064013 A09854 A09850 A249167 小精灵 A251237 A251411 A251412 A251413 A251542 A251543 A251544 A251545 A251546 A251547 A251554 A251555 A251556 A251557 A251558 A251559 A251604 A251621 A251756 A25837 A2528 A25865 A25867 A2528 A253048 A253049


Received March 7 2015; revised version received June 10 2015. Published in Journal of Integer Sequences, June 13 2015.


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