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1¡B11¡B21¡B1211¡B111221¡B312211¡B13112221¡B1113213211¡B31131211131221¡B...... (OEIS A005150)

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°_©l¬° 1¡A²Ä¤G¶µ¬O´y­z²Ä¤@¶µªºµ²ªG¡A§Y¦³ 1 ­Ó 1¡F²Ä¤T¶µ¬O´y­z²Ä¤G¶µªºµ²ªG¡A§Y¦³ 2 ­Ó 1¡F²Ä¥|¶µ¬O´y­z²Ä¤T¶µªºµ²ªG¡A§Y¦³ 1 ­Ó 2 ©M 1 ­Ó 1¡G¦p¦¹¤U¥h¡C

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²Ä¤TÂI«h¥Î¦h¤@¤BÂI®É¶¡¨Ó¸ÑÄÀ§a¡I­Y¯uªº¥X²{ 4 (©Î¥H¤Wªº¼Æ¦r)¡A¥²µM¦b«e¤@¶µ¥X²{¤F 4 (©Î¥H¤Wªº¼Æ¦r) ©Î¬O³sÄò¥X²{¤F 4­Ó (©Î§ó¦h­Ó) ¬Û¦Pªº¼Æ¦r¡C·íµM²Ä¤@­Ó¥i¯à©Ê³Ì²×±À¾Éªº·½ÀY¤]¬O²Ä¤G­Ó­ì¦]¡A¦]¬°¶}©l¬° 1 ¡A¤£·|µL¬G¥X²{ 4 ©Î¥H¤Wªº¼Æ¦r¡C¦ý°ÝÃD¬O·|¤£·|¦³ 4­Ó (©Î§ó¦h­Ó) ¬Û¦Pªº¼Æ¦r³sÄò¥X²{©O¡H¨º´NÅý§Ú­Ì¥ý¬Ý¬Ý¦³ 4 ­Ó¬Û¦P¼Æ¦rªº±¡ªp§a¡I

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2
2, 12, 1112, 3112, 132112, 1113122112, 311311222112, ......
3
3, 13, 1113, 3113, 132113, 1113122113, 311311222113, ......
4
4, 14, 1114, 3114, 132114, 1113122114, 311311222114, ......
d
d, 1d, 111d, 311d, 13211d, 111312211d, 31131122211d, ......

¤Wªí¤¤ d ¬° 2 ¦Ü 9 ¥ô¦ó¤@¼Æ¡C§Ú­Ì¤£Ãøµo²{·í¤¤ªº¦@³q¡C

­ì¨Ó³o¨Ç¼Æ¦Cªº¼Æ­È¬O·|º¥ªñ¤@¥N¼Æ¦¡ T(n) = ¡A

¦¡¤¤ªº = 1.567......¡B= 1.814...... ¡B = 1.3035772690342963912570991121525518907307025046594...... ¡A³o ¤SºÙ¬°±d­³±`¼Æ (Conway's Constant) (OEIS A014715)¡A¦Ó³o±`¼Æ³º¬O

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·í¤¤¥ç¦³¼Æ¾Ç®a§ä´M³sÄòªº´y­z¯À¼Æ (Descriptive Prime)¡A©Î·|§_¥X²{¥þ¯Àªº´y­z¼Æ¦C©O¡H¨ä¤¤±d¯Ç¥d (G. L. Jr. Honaker) «K§ä¨ì 373, 131713, 111311171113, 3113331173113 ³o¤@¼Æ¦C¡A¥i±¤¨ä¤U¤@¶µ¬O¤@¦X¼Æ¡C¦Ó¦b 2003¦~¡A¨½¥±µØ (Carlos B. Rivera, 1950- )¡B°ò«ä (Mike Keith) ©M µØ¹F¡DµÎ¥§¹F (Walter Schneider) §ä¨ì¤@ªø¤C¶µªº´y­z¼Æ¦C©l¦Û 19972667609¡C·|§_¦³§óªøªº¥þ¯Àªº´y­z¼Æ¦C¡H§Ú¬Û«H·|¦³ªº¡C

 

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Rivera, C. "Problems & Puzzles: Puzzle 036-Sequences of descriptive primes." http://www.primepuzzles.net/puzzles/puzz_036.htm

Schneider, Walter. "Descriptive Primes" http://www.wschnei.de/digit-related-numbers/descriptive-primes.html

Weisstein, E. W. "Look And Say Sequence." From MathWorld http://mathworld.wolfram.com/LookandSaySequence.html .

½Í²»¬f. "®¶Àú»P¼Éº¦ªº»y¨¥¼Æ¦C" ¦Û ¼Ö¦b¨ä¤¤ªº¼Æ¾Ç , ¥_¨Ê : ¬ì¾Ç¥Xª©ªÀ , p. 333-335 , 2005

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