"소모스 수열(Somos sequence)"의 두 판 사이의 차이

2011년 2월 24일 (목) 14:12 판

\(a_{n+4}a_{n} = a_{n+3} a_{n+2} + a_{n+1}^2\)
1, 1, 1, 1, 2, 3, 7, 23, 59, 314, 1529, 8209, 83313, 620297, 7869898, 126742987, 1687054711, 47301104551, 1123424582771, 32606721084786

RecurrenceTable[{a[n] a[n - 4] == a[n - 1] a[n - 3] + a[n - 2]^2,
a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1}, a, {n, 10}]

\(a_{n+5}a_{n} = a_{n+4} a_{n+1} + a_{n+3} a_{n+2}\)
1, 1, 1, 1, 1, 2, 3, 5, 11, 37, 83, 274, 1217, 6161, 22833, 165713, 1249441, 9434290, 68570323, 1013908933

RecurrenceTable[{a[n] a[5 + n] ==
a[2 + n] a[3 + n] + a[1 + n] a[4 + n], a[1] == 1, a[2] == 1,
a[3] == 1, a[4] == 1, a[5] == 1}, a, {n, 20}]

@@ 7번째 줄: / 7번째 줄: @@
 <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요</h5>
-t<sub>n+5</sub> = (t<sub>n+4</sub> t<sub>n+1</sub> + t<sub>n+3</sub> t<sub>n+2</sub>)/t<sub>n</sub><br> with initial values (1,1,1,1,1).
+* 소모스 4,5,6,7 은 정수수열
+* 소모스 7,8은 정수수열이 아니다
-<math>t_{n+5} = (t_{n+4} t_{n+1} + t_{n+3} t_{n+2})/t_{n}</math>
@@ 32번째 줄: / 31번째 줄: @@
 #  RecurrenceTable[{a[n] a[5 + n] ==<br>    a[2 + n] a[3 + n] + a[1 + n] a[4 + n], a[1] == 1, a[2] == 1,<br>   a[3] == 1, a[4] == 1, a[5] == 1}, a,   {n, 20}]<br>
+* [http://www-groups.dcs.st-and.ac.uk/%7Ejohn/Zagier/Solution5.1.html ][http://www-groups.dcs.st-and.ac.uk/%7Ejohn/Zagier/Solution5.1.html http://www-groups.dcs.st-and.ac.uk/~john/Zagier/Solution5.1.html]
@@ 63번째 줄: / 66번째 줄: @@
 * http://www.cut-the-knot.org/arithmetic/algebra/SimpleSomosSequence.shtml
 * http://faculty.uml.edu/jpropp/somos.html
-* [http://www-groups.dcs.st-and.ac.uk/%7Ejohn/Zagier/Solution5.1.html http://www-groups.dcs.st-and.ac.uk/~john/Zagier/Solution5.1.html]
+*
 *  van der Poorten, Alfred J. 2004. Elliptic curves and continued fractions. math/0403225 (March 14). http://arxiv.org/abs/math/0403225. <br>  <br>